In a large skillet over medium-high heat, cook the ground beef until browned and cooked through, breaking it apart with a spoon as it cooks. Drain excess fat.
Transfer the cooked ground beef to the crock pot.
Add the diced tomatoes with green chilies, diced tomatoes, diced green chilies, diced yellow onion, minced garlic, ground cumin, chili powder, smoked paprika, black pepper, and salt to the crock pot. Stir to combine.
Cover and cook on low for 2 hours, stirring occasionally.
After 2 hours, add the processed cheese cubes, shredded sharp cheddar cheese, and milk to the crock pot. Stir well to combine.
Cover and continue cooking on low for an additional 1 hour, stirring every 15 minutes until the cheese is completely melted and the mixture is smooth and creamy.
Once fully melted and combined, taste and adjust seasoning if needed.
Serve warm with tortilla chips, crackers, or fresh vegetables.