In the bowl of a stand mixer whisk 1 cup of the all-purpose flour, 1/3 cup granulated sugar, and 2 (1/4-ounce) packets dry active yeast together. Heat 1 cup of the milk until warm to the touch (100°F to 110°F). Stir into the flour mixture that’s in your mixer bowl, until combined. Cover with a kitchen towel and let sit in a warm place until doubled in volume, about 30 minutes.

While the dough is rising, whisk 12 tablespoons melted unsalted butter and 1 1/2 teaspoons kosher salt together in a small bowl until combined. Then whisk in the 4 large egg yolks until fully combined.

Once the yeast mixture has doubled in volume, add in the egg yolk mixture and remaining 3 1/2 cups all-purpose flour. With the dough hook attachment on medium speed, knead until the dough is soft, smooth, and forms a ball, approximately 2 to 4 minutes. Cover and let rise in a warm place until doubled in volume, about 40 to 60 minutes.

Line a baking sheet with parchment paper. Punch the dough down, then transfer to a clean work surface. Divide the dough into 12 pieces that weigh about 3 ounces each, and cover with a kitchen towel or plastic wrap.

Working with 1 piece of dough at a time, roll or stretch the dough into roughly a 4×6-inch rectangle. Fold 1 American cheese slice in half and place on one long side of the dough, near the edge. Top the cheese with 2 pickled jalapeño slices if using, 1/12 of the cooked sausage, and 1/12 of the scrambled egg. Starting with the longer side where the fillings are, roll the dough over the fillings toward the other side. Pull and tuck the open ends under toward the seam, making sure the fillings are completely encased in dough.

Place the filled kolaches on the baking sheet seam-side down, spacing them apart evenly in 2 rows. Don’t worry if they are not very far apart.

Again, cover and let rise in a warm place until doubled in size, about 40 to 60 minutes. In the meantime, heat the oven to 375°F. In a small bowl whisk together the remaining tablespoon of milk and the reserved large egg white  until combined.

Brush the egg white mixture onto the kolaches.

Bake until the kolaches are golden brown and an instant-read thermometer inserted into the thickest part not touching the filling registers at least 195°F. This will take about 30 minutes. Check after 15 minutes and tent loosely with aluminum foil if the kolaches are browning too quickly. Let cool for at least 10 minutes before serving.