Preheat your oven to 425°F. While it heats, crack the eggs into a bowl and whisk together with room temperature milk, salt, pepper, nutmeg, and smoked paprika until well combined and slightly frothy. This ensures the eggs cook evenly and creates a lighter, more tender frittata. Set the egg mixture aside at room temperature.
Heat olive oil in a 10-inch oven-safe skillet over medium-high heat. Add the sliced mushrooms and minced garlic, cooking for 2-3 minutes until the mushrooms begin to brown and release their moisture—I like to let them get a little color on the edges for deeper flavor. Add the diced red onion and cook for another 1-2 minutes until softened. The mushrooms should be golden and the aromatics fragrant.
Add the spinach and rosemary to the skillet and stir constantly for 30-60 seconds until the spinach is just wilted but still bright green. This quick cooking preserves the spinach's color and nutrition while infusing the dish with the rosemary's aromatic oils. Once wilted, distribute the vegetables evenly across the skillet to create a uniform base for the eggs.
Reduce heat to medium and pour the egg mixture from Step 1 evenly over the sautéed vegetables from Step 3. Let it cook undisturbed for 4-5 minutes until the edges and bottom begin to set but the center is still slightly wet. You should see the edges pulling away from the sides of the skillet. Sprinkle the feta cheese over the top once the edges start to set.
Transfer the skillet to the preheated 425°F oven and bake for 5-7 minutes until the top is set but still slightly moist in the very center—the residual heat will continue cooking it as it rests. Remove from the oven and let the frittata rest for 5 minutes before slicing. This resting period allows the eggs to set completely and makes serving much cleaner.