Heat oven to 350 degrees.
Butter an 8x8 or similar baking dish or a 10" cast iron skillet.
In a large mixing bowl, add the eggs, Dijon mustard, Herbs de Provence, and diced onion. Whisk to combine.
Add the shredded zucchini then the shredded sweet potatoes, stir in the shredded cheese. Sprinkle the top with the flour and add the salt and pepper. Stir to combine and pour mixture into the buttered baking dish or cast iron skillet.
Bake uncovered for 40-50 minutes until set and golden brown on top.
*If preparing and assembling ahead of time and not baking. Refrigerate the baking dish until ready to bake, but add 15 minutes to the baking time and cover the baking dish for the first 15 minutes to prevent the top from getting too brown.
Let the egg bake rest for 5 minutes before cutting.