Heat oil in a medium saucepan over medium heat. Stir in onion and cook until softened, about 5 minutes. Add garlic and cook just until fragrant, about 1 minute.
Stir in tomato sauce, vinegar, sugar, adobo sauce, mustard, allspice, and salt. Bring mixture to a boil, reduce heat, and simmer 5 minutes. Add peaches and cook until starting to soften, 2 to 5 minutes.
Transfer to a blender and purée until smooth. Serve sauce with your favorite grilled meats and grilled peach halves.
Note: Nutritional analysis is per serving.