Charred-Eggplant and Beef Burgers

Heat grill to high. Char eggplant, turning often, until cooked through and soft, about 30 minutes. Let cool slightly.

Cut eggplant in half, and scrape flesh into a fine sieve set over a bowl; discard skin. Let stand for 2 hours to drain. Coarsely chop eggplant.

Stir 1/2 cup eggplant into beef; reserve remainder for another use. Divide mixture into 4 equal pieces. Shape each into a 3 1/2-inch patty (about 3/4 inch thick).

Reheat grill to high. Grill buns, cut sides down. Brush both sides of burgers with oil, and season with salt. Grill until charred, about 4 minutes per side for medium (3 minutes per side if using a grill pan).

Meanwhile, mix together ketchup, pickles, yogurt, and mustard. Spread some sauce onto each bun half. Top bottom buns with lettuce, tomato, then burgers. Shave cheese onto burgers using a Microplane zester. Sandwich with remaining bun halves.