Preheat the oven to 400 degrees F. Brush the bottom and sides of a 9 X 13 inch baking dish with 1 tablespoon melted butter.
Pour flour, 1 teaspoon salt, 1 egg, 1 1/2 tablespoon melted butter, and 2/3 cup water in a stand mixer bowl. Attach the bread hook and mix on low for 5 minutes, until the ingredients come together into a smooth tacky ball. Let the mixer run another 2-3 minute to knead the dough. If it seems too dry (not sticky) add 1-2 additional tablespoons of water. Brush the remaining butter around the dough ball and on the sides of the bowl. Then cover with plastic and let the dough rest for at least 15 minutes.
Meanwhile, in a separate bowl mix the cottage cheese, sour cream, 1 1/2 cups shredded white cheddar, 4 eggs, thyme, garlic powder, nutmeg, 1/2 teaspoon salt, and 1/2 teaspoon ground pepper together.
Divide the dough into 4 equal pieces. Lay one piece at a time on a clean work surface. Roll and stretch the dough into a 9 X 13 inch rectangle. (No need to flour the surface.) The dough should be thin enough to see light through it. Spread one-quarter of the cheese mixture over the dough. Then starting on a short end, gently fold the dough over 1 1/2 - 2 inches at a time, until it's rolled into a loose log. Carefully lift the log by the ends and lay it in the prepared baking dish.
Repeat with the remaining dough and cheese mixture. Once four logs are arranged in the baking dish, gently cut each log into 4 equal pieces. Pour half-and-half over the top and sprinkle on the remaining shredded cheddar.
Bake for 45-50 minutes, until the tops are puffy and golden, even in the center of the pan. Cut and serve!
NOTE: Don't have time to make your dough from scratch? Guess what, you can use lasagna noodles in this recipe. The texture isn't quite the same, but the flavor and cozy appeal is all there! Simple lay dried lasagna noodles in between 4 layers of the cheese mixture. Pour in the half-and-half, top with shredded cheese, and bake as directed.