Arrange an oven shelf to the middle position of the oven. Preheat oven to 350ºF (177ºC). Butter a 9X13 inch baking dish, or spray with nonstick cooking spray; set aside.
In a medium mixing bowl, stir together Cheddar-Bay Biscuit mix (1 package), seasoning packet, and water (3/4 cup). Spread it in the buttered baking dish. Bake in preheated oven for 10-12 minutes; set aside.
In a 12-inch skillet, brown the beef (2 pounds) in 2 batches until cooked through. Transfer the first batch to a plate and continue with the second batch. Transfer the second batch to a plate; set aside. Leave dripping in skillet.
Add onion (1/2 cup), poblano pepper (1/2 cup), and red bell pepper (1/2 medium) to skillet with dripping and sauté until vegetables are just soft, 5-6 minutes.
Stir in drained canned corn (1 can), taco seasoning (1 envelope), and salt (1 teaspoon) then stir until evenly combined. Add the browned beef and evenly combine.
Stir in the drained ranch beans (1 can), drained tomatoes (1 can), and green chiles (1 can) and combine evenly.
In another medium bowl, stir together mayonnaise (3/4 cup), sour cream (3/4 cup), and smoked paprika (1/2 teaspoon). Fold in 1 cup of the pepper Jack and 1 cup of Cheddar.
Arrange beef and vegetable mixture over baked biscuit base.
Spoon the mayonnaise mixture over beef, bean, and vegetables then use an offset spatula to gently spread to cover.
Sprinkle the top of the casserole with the remaining cheeses. Bake, uncovered, until the top starts to brown in spots, and the casserole is bubbling around the edges about 30 minutes. Remove from oven and let sit 10 minutes before serving.