Super Tuscan Burgers and Potato Salad with Capers and Celery

Name: Super Tuscan Burgers and Potato Salad with Capers and Celery
Ingredients: 2 1/2 pounds small waxy potatoes, quartered or halved, depending on size; Coarse salt; 3/4 pound ground pork; 3/4 pound ground veal; 3 tablespoons extra-virgin olive oil, plus 5 to 6 tablespoons, divided; 1/2 cup dry Italian red wine, divided; 1/4 medium yellow skinned onion, finely chopped; 3 tablespoons, 5 or 6 sprigs, chopped fresh sage leaves; 4 cloves garlic, chopped; Coarse black pepper; 1/2 pound cremini (baby portobello) mushrooms, sliced; 4 crusty rolls, split; 8 ounces Pecorino Romano, shaved with a vegetable peeler; 1 cup arugula leaves, 1/2 bunch, trimmed of stems; 3 tablespoons capers; 1 celery heart and greens, from the center of stalk, chopped; 1/2 medium red onion, finely chopped; 1 lemon, zested and juiced; 2 tablespoons red wine vinegar