Roughly chop the carrots, sweet potatoes, and zucchini. Place in a food processor and pulse until finely chopped.
In a large, deep pan heat the olive oil over medium high heat. Add the vegetables and sage, stirring often until tender and golden brown (about 10 minutes). Stir in salt and pepper to taste.
Level out the veggies with a spatula and lower heat to medium. Pour the eggs on top of the veggies and sprinkle with the cheese. Cover and cook until eggs have set and cheese is melted (about 5-8 minutes).