Warm the milk in a measuring cup to about 110 degrees. Add yeast and 1 teaspoon sugar. Stir until completely dissolved. Let the yeast proof until foamy, about 10 minutes.
Meanwhile, sift the 3¾ cups flour, 6 tablespoons sugar and salt into the bowl of a stand mixer. Add the egg yolks, melted butter, lemon zest and proofed yeast mixture and mix on lowest speed to incorporate all the ingredients, about 1 minute.
Increase the speed slightly and knead until very smooth, about 5 more minutes. (A blister on the surface of the dough is a good sign.) Remove the dough hook and scrape the dough off the walls of the bowl. The dough should not stick to the spatula. Leave dough in the bowl and sprinkle it with flour. Cover the bowl with plastic wrap and let it rise in a warm place until it doubles in size.
Once doubled, transfer the dough to a lightly floured work surface, divide in half, and roll out into two long cylinders. Divide each cylinder into eight equal pieces (2 ounces each) and form small balls. Before placing them on a baking sheet lined with parchment paper or a greased baking sheet sprinkled with flour, roll them in the excess flour on the table.
Do not crowd the kolaches; it will take two baking sheets to accommodate them. Press down on the balls with your palm to flatten them. Let them rise in a warm place (about 15 minutes). Flatten the risen buns again and make a deep indentation in the center of each. Brush the edges with Egg Wash. Put Cheese Filling in the middle, place fresh peaches on the top.
Sprinkle Streusel over peaches. Let the completed kolaches rise for an additional 15 to 20 minutes; meanwhile, heat oven to 350 degrees. Place trays, one at a time, on the middle rack of heated oven and bake 20 to 30 minutes. Brush the edges of the kolaches with melted butter. Cool slightly before serving.
For Egg Wash:
Combine egg yolks with milk and whisk with fork.
For Cheese Filling:
Combine cheese with sugar, egg yolk and lemon zest.
Mix the flour and sugar together. Rub the butter into the flour/sugar mixture to form a crumbly topping.