For the peppers:
½ lb. padron peppers
3 tablespoons olive oil
coarse salt, like Maldon or fleur de sel
For the burgers:
1 lb. ground chuck beef
1 lb. chorizo, casings removed
2 cloves garlic, finely diced
Kosher salt and pepper
Mayonnaise, sliced jack cheese, 4 burger buns (buttered and toasted, if desired)
On a baking sheet, toss the padron peppers with the olive oil. Roast the peppers in the oven at 450 degrees until the skins start to blacken in spots, and the flesh of the peppers start to collapse and soften, about 20-25 minutes. Sprinkle the peppers with coarse salt, and coarsely chop. Set aside.
To make the patties, gently mix the beef, chorizo, garlic, salt and pepper together in a mixing bowl. Divide the mixture into 4 patties. Grill the patties (or cook them in a cast iron pan on the stovetop) until cooked through, adding the cheese on top and covering the grill or pan so the heat melts the cheese.
Place each patty on a burger bun bottom, and slather the patty with mayonnaise. Top each patty with a spoonful of the roasted padron peppers, and the top of the bun.