Cut the buns into small cubes. Slice the cherry tomatoes in halves, chop the bell peppers and onions, and roughly chop the fresh parsley.
Mix oat milk, eggs, heavy cream, nutmeg, garlic powder, and onion powder thoroughly.
Preheat oven to 350°F (175°C).
Prepare a 9 x 13-inch casserole or three small-size baking dishes sprayed or brushed with cooking oil.
Arrange alternate layers of bread and vegetables, starting with bread from the bottom of the casserole. Add a thin layer of grated cheese in between.
Pour the egg-cream mixture over the bread and let it soak for at least 10 minutes. Add grated cheese on top before baking.
Bake the strata for about 35-40 minutes until the top is golden brown and the center is set. If you’re uncertain, give the dish a little shake—if the middle jiggles, it needs a few more minutes. Serve Warm.