Cook the rice according to the instructions on the package. Once cooked, drain any excess water. Stir in lime juice, cilantro, and season with salt to taste.
Cook beef: Heat a skillet or nonstick pan over medium heat then add beef, chili powder, cumin and paprika. Season with salt and pepper and cook while breaking it up into smaller pieces until beef is no longer pink, about 6 minutes.
Make quesadillas: Heat a large nonstick pan over low medium heat. When the pan is hot, add a tortilla and 1/2 cup of cheddar cheese all over. Top with a second flour tortilla and cook until the cheese has melted, about 2 minutes per side. Repeat with for remaining portions.
Build quesaritos: Working on a cutting board or plate, top the center of one quesadilla with some rice, meat, 1/4 cup of cheese and sour cream. Fold in the ends and roll up tightly into a burrito. Repeat for all portions.
Reheat the nonstick pan over medium-high heat. When the pan is hot, add two quesaritos and cook until the outside quesadilla is golden and slightly crispy, 3 to 5 minutes per side. Serve immediately.