Preheat the oven to 350 degrees F (175 degrees C). Grease a 2-quart casserole dish.
Melt butter in a skillet over medium-low heat. Add garlic; stir in onion, sweet peppers, and green bell pepper. Cook until tender, about 5 minutes. Add mushrooms and cook until tender, 4 to 6 minutes. Add green chiles and stewed tomatoes; cook until heated through, 3 to 4 minutes. Season with salt and pepper. Spread mixture over the bottom of the prepared casserole dish.
Whisk soy milk and eggs together in a large bowl until well blended. Add flour, cilantro, oregano, and cumin. Season with salt and pepper. Blend very well with the whisk until most of the lumps are gone.
Sprinkle 1/2 cup Cheddar-Monterey Jack cheese blend on top of pepper mixture in the casserole. Pour in egg mixture and top with remaining cheese.
Bake in the preheated oven until a fork inserted in the middle comes out clean and the top and sides are just beginning to crisp, about 45 minutes. Cool for 10 minutes before serving.