For the dough: Whisk together the warm milk, yeast and 2 teaspoons sugar in the bowl of a stand mixer fitted with a dough hook. Allow to sit until it begins to bubble, about 5 minutes. Turn the mixer to medium and add the salt and eggs. Mix until the eggs are incorporated. Add the remaining 1/4 cup sugar, then reduce the speed to low and add the flour in batches, allowing the flour to fully incorporate with the dough between additions. Continue to mix until well combined. Add the butter in small pieces, allowing each addition to become fully incorporated before adding more. Turn the mixer to medium and let the mixer knead the dough for 10 minutes. Spray a large bowl with cooking spray. Place the dough in the bowl, cover with a towel or plastic wrap and allow to rise until it has doubled in size, about 1 hour.
For the filling: Spray a 12-cup muffin tin and set aside. Turn the dough onto a floured surface and use a rolling pin to roll it out into a 12-by-18-inch rectangle. Brush the olive oil over the dough and sprinkle with the chile flakes, garlic, Gruyere, pine nuts and oregano. Starting from the longer side, roll the dough up tightly, similar to how you make a cinnamon roll, and pinch the edges to seal, placing it seam-side down. You should have an 18-inch log. Cut into 24 slices, then smush two slices into each muffin cup, cut-side up and overlapping. (This whole process is a little messy and rustic but when they bake and rise they will look beautiful.) Cover with a kitchen towel and set aside for 30 minutes.
To finish: Preheat the oven to 375 degrees F.
Beat the egg together in a small bowl with 1 tablespoon water. Brush the tops of the muffins with the egg wash and sprinkle with flaky salt, pepper and Parmesan. Bake until puffed and golden, 15 to 20 minutes. Allow the muffins to cool slightly, then use a sharp paring knife to run around the edges to release them from the tin.