In a large skillet, melt the butter over medium-high heat then add the onions and zucchini and cook, stirring for 6 minutes. Add the mushroom and cook, stirring until the liquid is absorbed and the vegetables are wilted, about 10 minutes. Add the garlic and cook for 1 minute.
Add the tomatoes, basil, and thyme then season with salt and pepper and cook, stirring 1 minute. Remove from the heat and cool.
In a bowl, beat the eggs and milk together, add the grated cheese and red pepper flakes.
Place the pie crust in the pie pan. Add the vegetable mixture. Pour the egg mixture on top. Top with the goat cheese.
Bake for 25-30 minutes or until the eggs are set and browned. Remove from the oven and let stand 5 minutes before slicing.