Cook spinach in 1/4 cup of water in a covered saucepan until just wilted, a couple minutes. Drain water and set aside.
In a mixing bowl, whisk together eggs, Parmesan cheese, and milk. Add in chopped sun-dried tomatoes, and sprinkle with salt and pepper. Set aside.
Sauté onions in olive oil in an ovenproof, stick-free skillet, until translucent, about 4-5 minutes on medium heat. Add garlic and cook a minute further. Add cooked spinach and mix in with onions and garlic.
Spread out spinach mixture evenly on bottom of skillet. Pour egg mixture over spinach mixture. Use a spatula to lift up the spinach mixture along the sides of the pan to let egg mixture flow underneath.
Sprinkle bits of goat cheese over the top of the frittata mixture. When the mixture is about half set, put the whole pan in the oven. Bake for 13-15 minutes, until frittata is puffy and golden.
Remove from oven with oven mitts and let cool for several minutes. Cut into quarters to serve. Be careful of the handle since it stays hot for some time.