Preheat the oven to 350 degrees F (180 degrees C). Lightly coat a 9x13-inch baking dish with cooking spray.

Stir baking mix, milk, and 1 tablespoon oil together in a bowl. Spread evenly in the prepared baking dish.

Bake in the preheated oven until just starting to turn golden brown, 10 to 15 minutes. This step is just par-baking - this layer will not be fully baked at this point. Remove from the oven and set aside.

Heat remaining tablespoon oil in a large skillet over medium-high heat. Add ground beef and cook, stirring occasionally, until almost cooked through, about 4 minutes.

Add onion and poblano, stirring occasionally, until the beef is cooked through and onions begin to soften, about 4 minutes more. Stir in taco seasoning and salt until evenly combined. Remove from heat; set aside.

Add mayonnaise, sour cream, 1 cup pepper Jack cheese, and 1 cup Cheddar cheese to a bowl; stir until well combined.

Spoon beef mixture evenly over par-baked biscuit in the baking dish. Sprinkle drained diced tomatoes evenly over beef. Carefully spoon mayonnaise mixture over beef and tomatoes. Sprinkle evenly with remaining shredded cheese.

Bake, uncovered, until cheese is bubbly and starting to turn golden brown, about 30 minutes.

Let the dish rest for 10 minutes before serving. Garnish with sour cream and cilantro or green onions.