Preheat the oven to 350°F (175°C). Lightly grease a deep 9x13-inch baking dish and set aside.
Heat the olive oil in a large skillet over medium-high heat. Add the chopped onion and cook about 2 minutes until softened.
Add the ground beef to the skillet and cook, breaking it up, until fully browned; drain any excess grease.
Return the skillet to medium heat. Stir in the minced garlic, chili powder, cumin, smoked paprika, dried oregano and 1 teaspoon salt, then add the tomato paste and cook 1 minute more.
Stir in the refried beans, 1 1/2 cups salsa, 1/2 cup water and the chopped green chilies. Cook, stirring, until the mixture is smooth and combined; add cayenne if you want more heat. Taste and adjust seasoning, then remove from heat.
In a medium bowl, whisk together the sour cream, softened cream cheese, 1/2 cup salsa verde and a pinch of salt until smooth to make the creamy filling.
Combine the Monterrey Jack and sharp cheddar cheeses in a separate bowl and set aside.
Optionally char the tortillas briefly over a gas flame or in a hot skillet until lightly browned in spots for extra flavor.
Spread 1/2 cup salsa in an even thin layer on the bottom of the prepared baking dish.
Form the first tortilla layer by placing 2 whole tortillas in the center and surrounding them with six halved tortillas to cover the dish surface.
Spread one-third of the creamy filling over the tortillas, sprinkle with 1 cup of the combined cheeses, then spoon one-third of the meat mixture on top.
Repeat two more times with tortillas, one-third of the creamy filling, 1 cup cheese and one-third of the meat so you have three layered sections total.
Top with a final layer of tortillas, spread the remaining salsa over the top, and sprinkle with the remaining cheese.
Cover the dish and bake for 30–40 minutes, until heated through and the cheese is melted. Let the casserole rest 10 minutes before slicing.
Serve slices topped with lettuce, tomatoes, olives, avocado, cilantro, jalapenos and additional sour cream or crushed Doritos if desired.