You'll preheat the oven to the broil setting for this recipe. Typically, broiling is done at high heat, which is around 500°F (260°C). However, ovens can vary, so it's essential to keep an eye on the frittata while broiling to prevent burning.
In a bowl, whisk together the eggs, milk or cream, salt, and pepper until well combined. Set aside.
Heat olive oil in an oven-safe skillet over medium heat. Add the chopped onion and sauté until translucent, about 3-4 minutes.
Add the asparagus pieces to the skillet and cook until tender-crisp, about 5-6 minutes.
Pour the egg mixture evenly over the asparagus and onion in the skillet. Sprinkle crumbled goat cheese and chopped parsley on top.
Cook the frittata on the stovetop for 3-4 minutes, or until the edges start to set.
Transfer the skillet to the preheated oven and broil for 3-5 minutes, or until the top is set and lightly golden brown.
Remove from the oven and let the frittata cool slightly before slicing and serving. Optionally, sprinkle grated Parmesan cheese on top before serving.