In medium bowl, combine tomatoes, onion, vinegar, basil, salt and pepper; mix well. Let stand at room temperature for 20 minutes to blend flavors.
Meanwhile, shape ground beef into 8 patties, 4 inches in diameter. Spread 1/2 teaspoon mustard on each of 4 patties; top mustard with feta cheese. Top each with remaining patty. Seal patties by pressing edges together.
Spray broiler pan with nonstick cooking spray. Place patties on pan. Broil 4 to 6 inches from heat for 3 minutes. Carefully turn burgers; broil an additional 3 to 5 minutes or until no longer pink in center.
To serve, place burgers on bottom halves of buns; spoon 1/4 of tomato mixture over each burger. Cover with top halves of buns.