Prepare the Sauce
If using homemade sauce, mix brown sugar, mustard, and ketchup in a bowl until well combined. This creates a balanced sweet and tangy base for your sloppy joe filling. Set aside until needed.
Cook the Meat
Cook the ground beef in a large skillet over medium-high heat, breaking it apart with a spatula until fully browned, about 5-7 minutes. Drain excess fat and return the meat to the skillet. Add either the Manwich sauce or your homemade sauce to the meat mixture. Bring to a boil, then reduce heat and allow the mixture to simmer for 5 minutes, letting the flavors meld together.
Heat the Pan
Heat a separate skillet or sauté pan on medium heat. Add oil to the pan and allow it to get hot, but not smoking. This ensures your quesadilla will get crispy without burning.
Assemble the Quesadilla
Place one flour tortilla in the heated pan. Spread approximately 1/4 of the prepared meat mixture evenly over the tortilla, leaving a small border around the edge. Top with a portion of grated muenster cheese and cover with another tortilla, pressing down gently to seal.
Cook First Side
Cook the quesadilla for 3 to 4 minutes until the bottom tortilla is golden brown and crisp. Check occasionally by lifting an edge with a spatula to monitor browning.
Flip and Complete Cooking
Carefully flip the quesadilla using a large spatula and cook the other side until browned and crispy, approximately 3 to 4 more minutes. The cheese should be completely melted. Transfer to a cutting board and repeat the process with the remaining ingredients to make 4 quesadillas total.
Serve
Cut each cooked quesadilla into quarters or wedges using a pizza cutter or knife. Serve immediately while hot and crispy for the best texture and flavor.