How to Make It
In a bowl, combine the vinegar and sugar with the crushed red pepper and 1 teaspoon salt. With a vegetable peeler, cut the zucchini into ribbons; add to the vinegar mixture and let stand 10 minutes.
Meanwhile, heat grill to medium-high. Form the beef into four ¾-inch-thick patties. Use your fingers to make a shallow well in the top of each patty. (This will prevent overplumping during cooking.) Season with a total of ½ teaspoon each salt and pepper.
Oil the grill and cook the patties with the wells facing up for 4 to 5 minutes. Flip and cook until an instant-read thermometer inserted in the center registers 155° F for medium, 4 to 5 minutes more. Form sandwiches with the buns, radicchio, burgers, ricotta salata, and pickled zucchini.