Mix the brown sugar, mustard, and ketchup in a bowl until smooth if using the homemade sauce. Set aside.
Heat a large skillet over medium heat, about 350°F. Add the ground beef and cook for 6 to 8 minutes, breaking it up as it browns. Once fully cooked with no pink remaining, drain excess fat and return the beef to the skillet.
Stir in the Manwich sauce or homemade sauce. Bring to a gentle boil, then reduce heat to low and simmer for 5 minutes, until the meat is evenly coated and slightly thickened. If the mixture looks too thick, add 1 to 2 tablespoons of water.
Wipe out the skillet and return it to the stove over medium heat. Add the oil and heat until it shimmers without smoking.
Place one tortilla in the skillet. Spread an even layer of the sloppy joe mixture over it, leaving a small border around the edge. Sprinkle with grated muenster cheese and top with another tortilla.
Cook for 3 to 4 minutes until the bottom tortilla is crisp and golden. Flip carefully and cook the other side for another 3 to 4 minutes, until the cheese is melted and the tortillas are lightly blistered.
Repeat with the remaining tortillas, meat, and cheese. Transfer to a cutting board, slice into wedges, and serve hot.