Place the bell pepper, jalapeno pepper, and onion into the bowl of a food processor. Puree until smooth.
Stir together 4 teaspoons of this mixture the mayonnaise, and vinegar in a small bowl. Season with pepper, garlic powder, and cumin. Cover and refrigerate for at least 3 hours.
Brown ground beef in a large skillet over medium-high heat. The drain of any excess grease. Stir in the taco seasoning with 1 ¼ cups of water. Reduce heat and simmer until the water is almost gone and the mixture is thick.
Layout a gordita shell onto a microwave safe plate. Spread a layer of Mexican cheese blend over the top of the gordita.
Place into the microwave and microwave for 30 seconds or until the cheese has melted. Place a taco shell onto one side of the gordita. Fold the gordita around the taco shell and press so it sticks to the cheese.
Add some ground beef to the taco shell and top with some of the sauce, romaine lettuce, and cheddar cheese.