Preheat oven to 350°. Line a 13x9-inch rimmed baking sheet with heavy-duty aluminum foil.
Place tomatoes and shallots on prepared pan.
In a small bowl, combine 2 tablespoons molasses, olive oil, ½ teaspoon salt, and ¼ teaspoon pepper. Using a pastry brush, brush molasses mixture onto both sides of tomatoes and shallots. Bake for 1 hour.
In the work bowl of a food processor, combine tomatoes, shallots, remaining 1 tablespoon molasses, remaining ¼ teaspoon salt, remaining ¼ teaspoon pepper, and vinegar. Pulse to desired consistency.
