Preheat the oven to 160°C.
Mix together the milk, eggs, paprika, cayenne and sprinkle with salt and pepper. Cut the chillies in half and add a single layer them on the bottom of a 9-by-13-inch baking dish.
Top the chiles with half the cheese. Repeat with another layer of chillies and another layer of cheese. Pour the egg mixture over the top.
Place the baking dish into a larger baking dish or on a rimmed baking sheet. Pour in 1/2-inch of water and bake until completely set, 35 to 45 minutes.
Cut into squares and serve with warm corn tortillas.