Preheat oven to 400°F.
Spray sweet potato chunks with cooking spray and roast in the oven until tender, about 30 minutes, tossing at the halfway point.
Meanwhile, cook sausage in a large skillet over medium-high heat until no longer pink, about 5-7 minutes. Transfer sausage to a bowl and add 2 teaspoons of oil to the same skillet. Once hot, add onion, red bell pepper and mushrooms to the skillet. Cook until onions are translucent, about 6-7 minutes, then add kale. Cook for another 2-3 minutes to allow kale to wilt. Remove from heat and transfer veggies to the bowl with the sausage.
Add to the roasted sweet potato into the bowl as well.
Whisk eggs, milk, thyme, garlic, salt and pepper together in a medium bowl. Add egg mixture to the sausage and veggie mixture. Pour into a large baking dish (9 X 13) sprayed with cooking spray.
Bake in the preheated oven until set, about 20 to 25 minutes, but the cook time will depend on the size of your baking dish. Let stand for 5 minutes and serve.
Store leftovers in an air-tight container in the fridge for 4-5 days.