Danish Meatball Burgers with Pickled Red Cabbage

Name: Danish Meatball Burgers with Pickled Red Cabbage
Ingredients: 1/2 cup white vinegar; 1/2 cup sugar; Kosher salt; 1/2 small red cabbage, thinly sliced; 1 tablespoon red currant jam; 1/2 cup mayonnaise; 1 tablespoon whole-grain mustard; 1 tablespoon dill pickle relish; 1 tablespoon capers; 1 teaspoon curry powder; 1 teaspoon ground turmeric; 1 small onion, minced; 2 pounds lean ground beef sirloin; 1/2 cup half-and-half; 1/4 cup breadcrumbs; 1/2 teaspoon freshly grated nutmeg; Kosher salt and freshly ground pepper; 2 tablespoons extra-virgin olive oil; 6 slices havarti cheese; 6 rye buns, split