Start by heating a large skillet over high heat. Add the lean ground beef and cook until a deep brown crust forms on about half the beef. Stir to break it apart, letting the crust add rich flavor. Once fully cooked, drain the fat and set the beef aside.
Add a tablespoon of butter to the skillet, then toss in the onions and bell peppers. Cook for a couple of minutes until caramelized and fragrant. Stir in minced garlic for that irresistible aroma.
Return the beef to the skillet. Stir in mustard, ketchup, brown sugar, salt, and pepper. Cook the mixture on medium heat until thickened and about 75% of the liquid is gone. This step creates that sticky, flavorful goodness.
Spread butter on one side of each bread slice. Lay 6 slices butter-side down on a cutting board, then place a slice of cheese on each. Top with a generous scoop of the beef mixture, another slice of cheese, and finish with the remaining bread slices, butter-side up.
Heat your griddle or skillet on medium-high. Place each sandwich on the hot surface and grill for 3-5 minutes per side, pressing down gently with your spatula. The bread should turn golden and crispy, while the cheese melts perfectly.