Preheat the oven to 375°F (190°C). Grease a 9 x 13-inch baking pan with cooking spray and set it aside.
In a large bowl, whisk together the beaten eggs, flour, evaporated milk, hot sauce, paprika, onion powder, and salt until well combined. Set this mixture aside.
In a large skillet, brown the ground beef over medium heat with the chopped onions until the onions are soft and the meat is nicely browned, which should take about 5 to 7 minutes.
Add the refried beans to the skillet with the beef and onions, mixing until everything is fully incorporated.
Cut the corn tortillas into 1-inch wide strips, then arrange half of the tortilla strips in a single layer at the bottom of the prepared baking pan.
Layer half of the green chilies evenly over the tortilla strips, followed by half of the grated cheese.
Repeat these layers with the remaining tortilla strips, green chilies, and cheese.
Pour the prepared egg mixture evenly over the top of the casserole.
Spoon the combined meat and bean mixture over the egg mixture layer.
Finally, sprinkle the remaining cheese over the top.
Cover the casserole with foil and bake in the preheated oven for 45 minutes. Remove the foil during the last 5 minutes of baking to allow the top to brown nicely.
Once the casserole is cooked through and bubbly, remove it from the oven and let it cool slightly before serving.