For the dough: Whisk together the warm milk, yeast and 2 teaspoons of the sugar in the bowl of a stand mixer fitted with a dough hook. Allow to sit until it begins to bubble, about 5 minutes. Start the mixer and add the salt and eggs. Mix until the eggs are incorporated.
Add the flour and remaining 1/4 cup sugar 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 fully incorporate before adding more. Leave the mixer running to continue kneading the dough for 10 minutes. Place the dough in an oiled bowl, then cover with a towel or plastic wrap and allow to rise until it has doubled in size, about 1 hour.
For the filling: Knead the dough on a floured surface for a few minutes to form a nice ball, then roll it out with a rolling pin into an 18-by-12-inch rectangle. Spread the olive oil over the dough and sprinkle with the Cheddar, sesame seeds, chile flakes, pine nuts, oregano and zaatar. Starting from the longer side, roll the dough up a quarter of the way at a time, similar to how you make a cinnamon roll, resulting in an 18-inch log. Cut the log in half, then slice each half into 12 pieces. Spray a muffin tin with nonstick spray, then flour it. Twist one piece of dough into a figure 8 and place in the muffin tin. Twist another piece and place in the same cavity—each muffin should be made of 2 pieces. Press down on the dough firmly to be sure it fits snugly. You will have 12 total muffins. Cover with a kitchen towel and set aside for 30 minutes.
Preheat the oven to 375 degrees F.
For the egg wash: Beat together the egg with 1 tablespoon water. Brush the tops of the muffins with the egg wash and sprinkle with zaatar and flaky salt. Bake until risen and golden, for 20 to 22 minutes. Allow muffins to cool at least 15 minutes, then use a sharp paring knife to run around the edges to release them from the pan.