Combine yeast and liquids in a small bowl: stir the yeast and a pinch of sugar into the warm milk and water. Let sit 5-8 minutes until foamy.

In a stand mixer, combine flour, sugar, and salt. Add the yeast mixture, egg, and softened butter. Mix on low until a shaggy dough forms, then increase speed and knead for 6-8 minutes until smooth and elastic. (If kneading by hand, knead for 10-12 minutes.)

Lightly oil a bowl, place the dough inside, cover with plastic wrap or a towel, and let rise in a warm spot until doubled, about 1 to 1 1/2 hours.

Whisk eggs with salt, pepper, and smoked paprika. Cook gently in a skillet over medium-low to make soft scramble - remove before fully firm as residual heat will finish them.

Stir in cheese, crumbled bacon or sausage, and chopped herbs. Let cool to room temperature.

Turn dough onto a lightly floured surface and divide into 12 even pieces. Flatten each piece into a 3-inch disc.

Spoon a tablespoon of the egg-cheese filling into the center of each disc. Fold edges up and pinch to seal, shaping into smooth balls. Place seam-side down on prepared baking sheet.

Cover shaped rolls with a towel and let them proof for 30-40 minutes until puffy.

Preheat oven to 375°F (190°C) during the last 10 minutes of proofing. Brush each roll lightly with the beaten egg wash and sprinkle sesame seeds if desired.

Place rolls in the preheated oven and bake for 18-22 minutes until golden brown and internal dough registers 190°F (88°C). Rotate pan halfway for even color. Cool slightly on a rack and brush with melted butter for sheen and flavor.

Let cool for 5 minutes before serving so the filling sets slightly. Enjoy with hot coffee, or add a side of fresh fruit for balance.