In a skillet, add avocado oil and onions. Cook on medium high heat until fragrant. Add in peppers, tomato, mushrooms, and green onions. Cook until tender, about 5-8 minutes. Add in garlic and cook another minute. Set aside.
In a large mixing bowl, whisk together eggs until pale yellow and fluffy. Mix in heavy cream, cheese, basil, salt, and pepper. Stir in mixed greens.
Pour vegetable mixture into a greased 9×13 baking dish. Pour egg mixture on top. Stir together until evenly spread in dish. Sprinkle with Parmesan cheese. Bake on 350°F for 50 minutes. Remove from oven and let rest for 10-15 minutes. Serve while warm and enjoy!