In a large bowl, mix thoroughly by hand the ground beef, the chorizo, the adobo seasoning, the grated onion and the bread crumbs. Form the burgers into 6 patties without pressing them too much or they can become tough. Line a baking pan with waxed paper and put the burgers side-by-side in a single layer. Cover and refrigerate for at least 30 minutes. This will help the burgers hold together. If you make more than you need just separate with waxed paper and insert into a storage freezer bag for future use.;
Heat the olive oil in a heavy skillet over medium-low heat. Add the onions and season with salt and pepper. Add the jalapeno chiles and the brown sugar. Saute for 15 minutes or until the onion and the chiles are caramelized and soft. Set aside.;
Drain the roasted red peppers and put them in a blender or food processor. Add the mayonnaise, and season with salt and pepper. Puree the mayonnaise and roasted red peppers until well combined and the mixture is smooth. NOTE: This may be done up to 2 days ahead of time, and in fact the flavor will be more complete with an overnight chilling.;
Preheat an outdoor grill or grill pan on the stove top over medium-high heat. Place the burgers on the hot grill or pan until cooked to desired doneness. Due to the raw chorizo in the recipe, at least medium-well is recommended, approximately 10 minutes on each side. In the last 5 minutes of cooking, top the burgers with the slices of cheese so it can melt. If your grill has a lid, putting it on briefly will help the cheese melt quickly and evenly.
To serve: Spread about 1 tablespoon of the red pepper mayonnaise on both sides of the rolls. Lay a burger on the bottom halves, and top with a couple of spoonfuls of the caramelized onion and jalapeno relish.