Combine the sugar, vinegar, tomato paste, sesame oil, molasses, soy sauce, and chili peppers in a small saucepan and bring to a boil. Reduce the heat to medium-low and simmer until it starts to become syrupy and dime-sized bubbles form, 12 to 15 minutes. Remove from the heat and transfer to a blender or food processor. Process on high speed until smooth.
Preheat the grill.
Using an oyster knife, shuck the oysters, drain off their liquor, and keep on the half shell, reserve the other half of the shells. Place the oyster on the half shell on the grill. Top each oyster with 1 heaping teaspoon of the sauce and cover with the other half of the shell. Grill until edges of the oysters start to curl, about 4 minutes. Remove from grill and serve immediately.