Preheat Oven & Prep PanPreheat oven to 350°F (175°C). Grease a 9×13-inch casserole dish.
Cook the VegetablesHeat oil in a large pan or Dutch oven. Add onion, bell pepper, and sweet potatoes. Sauté 8–9 minutes until slightly softened. Add garlic in the last 2 minutes. Spread evenly in casserole dish.
Cook the SausageUsing the same pan, cook turkey sausage until browned and crumbled. Drain excess liquid, then layer over the vegetables.
Mix the EggsIn a bowl, whisk together eggs, milk, thyme, salt, pepper, and cheese. Pour over the sausage and veggies, gently mixing so everything is coated.
BakeBake uncovered for 40–45 minutes, until the center is firm. If the top browns too quickly, cover loosely with foil.
Rest & ServeLet the casserole sit for 10 minutes before slicing. This helps the eggs set and makes serving easier.