Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish lightly with cooking spray or butter.
Open the cans of biscuit dough. Separate the biscuits and press them together into the bottom of the prepared baking dish, forming an even layer that covers the entire bottom. Use your fingers to seal any seams between biscuits. Brush the top lightly with the melted butter.
In a large skillet over medium-high heat, cook the ground beef, breaking it up with a spoon, until it is no longer pink, about 8-10 minutes. Drain excess fat. Add the diced onion, red and green bell peppers, and garlic to the skillet. Cook for another 5-7 minutes, until the vegetables have softened. Stir in the taco seasoning and water, then add the drained diced tomatoes with green chilies. Simmer for 3-4 minutes until the mixture thickens slightly. Remove from heat.
Spread the cooked beef and vegetable mixture evenly over the biscuit layer in the baking dish.
In a medium bowl, mix the sour cream with 1 cup of the shredded cheddar cheese. Spread this mixture evenly over the beef layer. Sprinkle the remaining 1 cup of cheddar cheese and the 1 cup of Monterey Jack cheese over the sour cream layer. Top with sliced black olives (if using).
Place the baking dish in the preheated oven and bake for 25-30 minutes, or until the cheese is fully melted, bubbly, and starting to turn golden brown, and the biscuit crust is cooked through.
Remove the casserole from the oven and let it rest for 10 minutes. This allows the layers to set for cleaner slicing. Garnish with sliced green onions. Slice into portions and serve directly from the baking dish.