In a small saucepan, mix together the first amount of bread flour, milk, and water. Place over medium heat and stir the mixture while it cooks and thickens. Once it reaches a paste-like consistency, remove it from the heat and set it aside to cool.

Combine the second amount of bread flour, sugar, yeast, and salt in a stand mixer bowl. Mix together to combine the ingredients.

Whisk together the egg and second amount of milk. On medium speed, stream in the milk and egg mixture. Add the cooked flour starter and mixture to combine. Finally, add the softened butter and mix until it forms a smooth dough.

Knead on medium high speed for 10-12 minutes. The dough should be smooth and elastic. Check the gluten development with the window pane test.

Place the dough in a lightly grease bowl and cover with plastic wrap. Place the dough in a warm area for 1 hour until it doubles in size. Gently degas the dough and transfer to a lightly floured surface.

Divide the dough into 12 equal size pieces. Take one piece of the dough and gently flatten. Add a small amount of cheese and cracked black pepper. Fold the sides in towards the center and turn it over so the seam is now on the bottom. Roll the dough into a bun/ball shape. Repeat these steps with the rest of the pieces.

Place the balls on a lightly floured surface and cover. Let it proof in a warm place for 1 hour.

Preheat the oven to 350F.

Whisk the egg and brush each bun with the egg wash. Garnish each one with more grated cheese.

Bake for 20 minutes until golden brown.