Heat the olive oil in a large iron or other ovenproof skillet over medium-high heat. Add the olive oil, and when it is shimmering, add the sausage. Break up gently with a spatula, and brown the sausage, turning as necessary.
Add the carrot, garlic, onion, and bell pepper and saute until almost tender, stirring occasionally, about 5 minutes. Add the zucchini and spinach and saute a minute more. Remove from heat and set aside.
In a large bowl, beat the eggs and add sea salt and black pepper to taste. Pour eggs over the sausage and sauteed vegetables. Place in the oven and bake for 20 to 25 minutes or until the eggs are puffed up and nicely browned. Cut in to wedges and serve.