Combine maple syrup, soy sauce, vinegar, hot pepper flakes and 1/2 of minced garlic together in large sealable freezer bag. Pierce steak with a fork all over; add to bag with marinade. Refrigerate for 8 to 12 hours.
Remove steak from marinade, discarding marinade. Grill over medium-high heat for 10 to 14 minutes, turning at least twice, for medium-rare doneness 145°F(63°C). Let stand 5 minutes.
Meanwhile, melt butter with remaining garlic over low heat in skillet or in microwave; brush on both sides of bread. Place on bread on baking sheets and broil on both sides until just golden brown; keep warm. Thinly slice steak diagonally across the grain to yield about 24 slices. To assemble drape beef over warm toasts and top with a small spoonful of mayonnaise and a dab of chutney. Garnish with parsley or chives.