Corned Beef Burgers with Latke Buns

Name: Corned Beef Burgers with Latke Buns
Ingredients: 1 Granny Smith apple, peeled; 1/2 pound beets, trimmed and peeled; 3 tablespoons olive oil; 1 1/2 tablespoons chopped fresh dill; 1 1/2 tablespoons sherry vinegar; Kosher salt and freshly ground black pepper; 1/2 cup spicy brown mustard; 1 1/2 tablespoons prepared horseradish; 1 half sour pickle, minced; 2 pounds russet potatoes; 1 small yellow onion; 1/4 cup matzo meal; 1 large egg, lightly beaten; Vegetable oil, for frying; 1 pound sliced corned beef from a deli (not canned); 1 large egg; 2 tablespoons matzo meal; Vegetable oil, to coat the pan; Applesauce, for serving