Mix the Levain:

1. The evening before you plan to make the dough, mix the sourdough starter, water, and flour until combined. Cover the bowl and let the mixture rise at warm room temperature until doubled in size, about 8-12 hours, depending on the temperature in your kitchen.

Cook the Milk Roux (Tangzhong):

1. In a small saucepan, whisk together 42 grams of whole wheat flour and 210 grams of milk until no lumps remain.
2. Bring the mixture to a simmer over medium-low heat and continue whisking until the mixture has thickened. To determine when it is ready, run your whisk along the bottom of the pan. It should leave an indentation. This should take 5-10 minutes.
3. Pour the mixture into a small bowl, cover with plastic wrap, and allow to cool at room temperature.
4. The roux can be prepared the evening before, or the next morning, before mixing the dough.

Saute the Herb Oil:

1. In a skillet over medium heat, saute the butter and oil, until melted and foamy, 1-2 minutes.
2. Add the garlic, and cook an additional 1-2 minutes, stirring constantly, until lightly browned.
3. Stir in the herbs, and cook about 30 seconds.
4. Reserve 1 tablespoon of herb oil in a small bowl. To use for brushing the warm rolls.
5. Allow the remaining herb oil to cool before incorporating in the dough.

Make the Dough:

1. In the bowl of a stand mixer, add the levain and milk roux. Mix on low speed until thoroughly combined.
2. Drizzle in the herb oil and continue mixing on low speed until fully incorporated throughout the dough.
3. Add the egg, mix thoroughly.
4. In a separate bowl, whisk together the flours and sugar. Gradually add the flour mixture to the dough. Mix until you can gently pull a window pain without tearing the dough.
5. Cover and let rest 20 minutes. Sprinkle the salt over the top of the dough. Mix thoroughly. Add sprinkles of water, if needed, to dissolve the salt. Cover and let the dough rest for 1 hour at warm room temperature.
6. Gently press down the dough to degas it. Fold the dough by gently stretching and folding the edges into the center. Cover, and let the dough rest for an additional 1-1 ½ hours.
7. Remove the dough to a lightly floured counter. Fold it over itself to degas. Let rest 20 minutes.
8. To form the Christmas tree pattern, divide the dough into 30 equal portions. Form the rolls and place them on a parchment-lined rimmed baking sheet in the form of a Christmas tree starting with 1 roll at the top and ending with 4 rolls at the bottom for the base. You may need to adjust the dough balls as you go. You’ll only need 29 rolls to form the Christmas Tree. This leaves one roll for the baker to taste test.
9. When baking the rolls in a baking pan, divide the dough into 24 equal pieces. Cut all 4 corners of a piece of parchment and place in a 9×13-inch pan. Overlap the ends neatly in the pan so the parchment doesn’t make creases in the dough. Place the rolls in the baking pan.
10. Cover the pan or baking sheet tightly with plastic wrap and place directly in the refrigerator. Allow the rolls to retard overnight.
11. The next day, remove the rolls from the refrigerator 2-3 hours before you plan to bake. Note: If it’s cold in your kitchen, place the baking pan or sheet in the cold oven with a bowl filled with boiling water underneath. Remove the rolls before you preheat the oven.
12. Preheat the oven 375 F during the final 20 minutes of proofing.
13. Optional egg wash: In a small bowl, whisk together 1 egg and 1 teaspoon of water. Uncover the rolls and brush them lightly with the egg mixture.
14. Bake the rolls on the middle rack of the oven for 10 minutes, rotate and bake an additional 10 minutes. Move the rolls up a rack, if needed for browning, and bake an additional 3-5 minutes until the rolls are a golden brown color. Total bake time 20-25 minutes.
15. Brush the top of the rolls with the reserved tablespoon of herb oil. Reheat the herb oil and drizzle in more olive oil, if needed, to make it more spreadable. Serve the rolls warm.