Stage 1: Prepare Oven and Roast Vegetables : Position an oven rack in the center and preheat to 375°F (190°C). On a baking sheet, toss the halved tomatoes and diced red bell pepper with 1 tablespoon of the olive oil and a pinch of salt. Arrange them in a single layer and roast for 15 minutes until they begin to soften and concentrate in flavor.
Stage 2: Form the Egg Custard : While the vegetables roast, crack the 12 eggs into a large mixing bowl. Add the grated Parmesan, 1 cup of the shredded mozzarella, the chopped dill, kosher salt, and red pepper flakes. Whisk vigorously until the mixture is uniform in color and slightly frothy. Set this aside.
Stage 3: Sauté Asparagus and Mushrooms : Place your 12-inch oven-safe skillet over medium-high heat and add the remaining 2 tablespoons of olive oil. Once shimmering, add the sliced mushrooms and cook for 4-6 minutes, allowing them to brown without stirring too frequently. Add the asparagus pieces and minced garlic, and continue to sauté for another 4 minutes until the asparagus is bright green and tender-crisp.
Stage 4: Combine and Assemble : Remove the skillet from the heat. Pour the prepared egg custard evenly over the sautéed asparagus and mushrooms. Gently stir once to ensure the vegetables are evenly distributed. Scatter the roasted tomatoes, peppers, and all the crumbled feta cheese over the surface.
Stage 5: Bake Until Set : Transfer the skillet to the preheated oven. Bake for 15-18 minutes, or until the frittata is puffed and the center is just barely set (it should have a slight jiggle). An instant-read thermometer inserted into the center should register 165°F (74°C).
Stage 6: Final Melt and Rest : Sprinkle the remaining ½ cup of mozzarella cheese over the top. Switch the oven setting to a low broil. Position the skillet about 6 inches from the heating element and broil for 2-3 minutes, just until the cheese is melted and develops a few lightly golden spots. Allow the frittata to rest in the skillet for 5 minutes before garnishing with extra dill, slicing, and serving.