Mix shrimp, tomatoes, ketchup, brown sugar, garlic and parsley. Add oil and vinegar. Season with salt and pepper. Keep covered and chilled.
Prepare grill and set rack 6 inches from heat. Lightly brush one side of each piece of bread with oil. Grill bread, oiled side up, for 1 minute. Turn and grill other side until lightly browned, 1 to 2 minutes.
Spoon a heaping tablespoon of shrimp mixture on top of oiled side of each bread slice. Garnish with whole shrimp, if desired.