Cut stem ends off tomatoes and cut tomatoes into 2 thick slices.
Put on broiler rack.
Combine sugar, basil, salt and pepper and sprinkle a little of mixture on each tomato slice.
Slip under hot broiler (about 4 inches from heat) and broil 2 minutes.
Add bread crumbs to melted butter and toss lightly with a fork.
Add blue cheese and toss again lightly.
Spoon on top of tomato slices and slip back under the broiler until crumbs are nicely browned, about 1 minute.