Cut each tomato in half, scoop out some of the seeds give them a squeeze to release some of the juice and drain. Put on broiler rack.
Combine sugar, basil, salt and pepper and sprinkle little of mixture on each tomato slice. Broil about 4-5 minutes. Add bread crumbs to melted butter and toss lightly with a fork. Add Stilton cheese and toss again lightly.
Spoon on tomato slices and slip under broiler until crumbs are nicely browned, about a 1 or 2 minutes. Serve Immediately. With nice crusty bread and a salad of peppery greens.