Step 1: Prepare the Levain (Optional – Skip if using only commercial yeast)

1. Combine Ingredients: In a small bowl, mix together the active sourdough starter, bread flour, and lukewarm water until a smooth, thick batter forms.
2. Ferment: Cover the bowl loosely with plastic wrap or a lid and let it sit at room temperature for 4-6 hours, or until it has doubled in size and is bubbly. This levain will add depth of flavor and improve the texture of your brioche.

Step 2: Combine Dry Ingredients

1. In a large mixing bowl (or the bowl of your stand mixer fitted with a dough hook), whisk together the bread flour, instant dry yeast (if using), salt, and granulated sugar. Ensure these dry ingredients are well combined to evenly distribute the yeast and salt.

Step 3: Incorporate Wet Ingredients (Except Butter)

1. Make a well: Create a well in the center of the dry ingredients.
2. Add Liquids and Eggs: Pour in the lukewarm milk, and crack in the eggs. If using the levain, add it to the bowl now as well.
3. Initial Mix: Using your hands or the dough hook on low speed, mix the ingredients until a shaggy dough forms. This will take a few minutes. Don’t worry if it looks a bit rough at this stage.

Step 4: Develop Gluten (Kneading)

1. Knead on Low Speed: If using a stand mixer, continue kneading on low speed (speed 2 on KitchenAid) for 8-10 minutes. If kneading by hand, turn the dough out onto a lightly floured surface and knead vigorously for 10-12 minutes.
2. Dough Consistency: The dough will initially be quite sticky, but as you knead, the gluten will develop, and it will become smoother and more elastic. Resist the urge to add too much extra flour, as this can make the rolls dry. The dough should be soft and slightly tacky to the touch.

Step 5: Incorporate Cold Butter – The Key to Brioche

1. Gradually Add Butter: With the mixer running on low speed (or while kneading by hand), add the very cold, cubed butter, one cube at a time. Allow each cube to be fully incorporated into the dough before adding the next. This process is crucial and will take time – be patient.
2. Dough Transformation: As you incorporate the butter, the dough will initially appear to break down and become even stickier. Don’t panic! Continue kneading, and the dough will eventually come back together, becoming smooth, glossy, and incredibly soft. This process can take another 10-15 minutes.
3. Check Gluten Development: To check if the gluten is sufficiently developed, perform the windowpane test. Take a small piece of dough and gently stretch it between your fingers. If it stretches thin enough to see light through it without tearing, the gluten is well-developed. If it tears easily, continue kneading for a few more minutes.

Step 6: First Proof (Bulk Fermentation)

1. Add Rosemary: Once the dough is smooth and elastic, add the finely chopped fresh rosemary and knead briefly to distribute it evenly throughout the dough.
2. First Rise: Place the dough in a lightly oiled large bowl. Turn the dough to coat it lightly with oil. Cover the bowl tightly with plastic wrap or a lid.
3. Proofing Time: Let the dough rise in a warm place (around 75-80°F or 24-27°C) for 1.5-2 hours, or until it has doubled in size. The exact proofing time will depend on the temperature of your kitchen. You can also do a slower, overnight proof in the refrigerator for enhanced flavor development – in this case, proof in the fridge for 12-16 hours.

Step 7: Divide and Shape the Rolls

1. Gently Deflate: Once the dough has doubled, gently punch it down to release the air. Turn the dough out onto a lightly floured surface.
2. Divide Dough: Divide the dough into equal-sized portions. For standard-sized rolls, aim for about 70-80g per roll. You can use a kitchen scale for accuracy. This recipe should yield approximately 12-15 rolls.
3. Shape into Rounds: Gently shape each portion of dough into a smooth round ball. You can do this by tucking the edges of the dough underneath and rolling it gently on the countertop until a smooth surface forms.

Step 8: Second Proof (Final Proof)

1. Arrange Rolls: Place the shaped rolls onto a baking sheet lined with parchment paper, leaving some space between them for expansion.
2. Second Rise: Cover the baking sheet loosely with plastic wrap or a clean kitchen towel. Let the rolls proof in a warm place for another 1-1.5 hours, or until they have almost doubled in size and are puffy and soft to the touch. This second proof is crucial for achieving light and airy rolls.

Step 9: Preheat Oven and Prepare Egg Wash (Optional)

1. Preheat Oven: Preheat your oven to 375°F (190°C) about 20 minutes before baking.
2. Egg Wash (Optional): In a small bowl, whisk together the egg and milk or water for the egg wash. This will give your rolls a beautiful golden-brown crust.

Step 10: Bake the Rosemary Brioche Rolls

1. Egg Wash (Optional): Gently brush the tops of the proofed rolls with the egg wash, being careful not to deflate them.
2. Bake: Place the baking sheet in the preheated oven and bake for 18-22 minutes, or until the rolls are golden brown on top and sound hollow when tapped on the bottom. Keep a close eye on them towards the end of baking to prevent over-browning.
3. Cool: Once baked, remove the rolls from the oven and let them cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely, or at least until they are warm enough to handle.

Step 11: Enjoy!

These Rosemary Brioche Rolls are best enjoyed warm, fresh from the oven. The aroma will be irresistible, and the taste will be even better!