Preheat oven to 350°F (175°C) and heavily grease a 9x13-inch baking dish with olive oil or non-stick spray.
Heat a tablespoon of olive oil in a large skillet over medium heat. Add the bell peppers, mushrooms, onion, and zucchini. Cook for about 5 minutes, until the vegetables are soft. Add spinach, and cook for another 2 minutes until the spinach wilts. Season with salt and pepper.
In a large bowl, whisk together the eggs, heavy cream (or almond milk), oregano, thyme, red pepper flakes, and a pinch of salt and pepper.
Spread cooked veggies evenly across greased baking dish. Sprinkle with shredded cheddar. Pour egg mixture evenly over top, making sure it covers all the ingredients. Sprinkle Parmesan cheese over top.
Place dish in oven and bake for 35–40 minutes or until eggs are fully set and top is golden brown.
Let casserole cool for 5 minutes before slicing and serving.