Preheat the oven to 350 degrees F.
For the roasted garlic sauce: Put a sheet of aluminum foil in a roasting pan and add the garlic. Toss with the oil, fold up the foil around the garlic and roast until soft, about 45 minutes.
For the beef patties: Toss the poblano peppers and onions with the vegetable oil and a pinch of kosher salt in a roasting pan. Cook for 30 to 35 minutes. Peel and seed the roasted peppers, then chop the peppers and onions into small dice.
When the garlic is done roasting, transfer to a blender, add the sour cream, mayonnaise and vinegar and blend until smooth. Season with salt and pepper. Set the sauce aside until serving.
Put the ground beef, Worcestershire, black pepper, ancho chile and 1 tablespoon kosher salt in a medium bowl. Fold in the diced peppers and onions. Divide the mixture into 3-ounce portions and form these portions into 8 patties.
Heat a griddle to medium or medium high; cook the patties to medium, about 5 minutes on each side.
For the corn and chorizo relish: Saute the chorizo in a skillet until lightly browned. Add the corn and cook for 5 minutes. Add the vinegar, then cook for another minute. Set aside.
For the griddled queso fresco and rolls: Heat a griddle to medium low. Grease the griddle with 1/2 teaspoon of the oil, then cook the cheese until golden brown, about 2 minutes on each side.
Grease the griddle with the remaining 1/4 teaspoon vegetable oil, then place the rolls on the griddle cut-side down until golden brown, about 2 minutes.
Place a burger on each roll, then spoon some of the corn and chorizo relish on top. Place a piece of griddled cheese over the relish, and top with some of the roasted garlic sauce.
Recipe courtesy of La Cocinita, New Orleans, LA