Cook the Meats: In a large skillet over medium heat, cook the ground beef until browned. Drain excess fat. Add chorizo and cook until fully browned, breaking it apart as it cooks.
Sauté the Vegetables: Stir in diced onions and cook until translucent (about 3 minutes). Add minced jalapeños and cook for another 2 minutes.
Combine Ingredients: Add diced tomatoes with green chilies, black beans, and corn. Stir well to combine.
Melt the Cheese: Reduce the heat to low and add the cubed Velveeta and shredded Pepper Jack cheese. Stir constantly until melted and smooth.
Season and Finish: Mix in ground cumin, chili powder, salt, and black pepper to taste. Stir in lime juice and sprinkle with chopped cilantro.
Serve Warm: Transfer the queso to a serving bowl and serve immediately with tortilla chips, bread, or as a topping for tacos and nachos.