Crack the eggs into a medium-sized bowl. Add the milk, salt, pepper, and fresh herbs to the bowl. Use a fork or whisk to vigorously beat the eggs together. Add the parmesan to the eggs and whisk once more.
Heat the olive oil and butter in a small oven-safe skillet over medium-low heat. Add the chopped greens and sauté for one minute, or until the greens are wilted. Add the acorn squash and caramelized onions to the pan and stir to evenly distribute the ingredients across the bottom of the pan.
Add the egg mixture to the pan and cook for two minutes without stirring.
Turn the stove off and put the pan in the oven. Allow the frittata to finish cooking for another 10-15 minutes, or until it is set and doesn't jiggle when you move the pan.
Allow the frittata to sit for five minutes before serving.