Preheat oven to 350 degrees F.
Combine tofu, non-dairy milk, chickpea flour, nutritional yeast, turmeric, and black pepper in a blender and process until smooth.
Pour into a 9x9 baking dish.
Fill each poblano with cashew cheese sauce and place in egg mixture, making sure there is one filled poblano in each quarter of the dish.
Drizzle any remaining cashew cheese sauce over poblano/egg mixture.
Bake for 1 hour.
Let sit 10-15 minutes before serving.