Prepare the Vegetables: Peel and chop the carrots, onion, and bell pepper into small chunks. Mince the garlic cloves.
Cook the Vegetables: In a saucepan, add the chopped vegetables, garlic, and water. Bring to a boil, then simmer for 20 minutes until the vegetables are soft.
Blend the Mixture: Allow the cooked vegetables to cool slightly, then blend the mixture into a smooth puree using a blender or food processor.
Combine the Ingredients: Pour the vegetable puree back into the saucepan. Add the vinegar, brown sugar, salt, pepper, mustard, turmeric, Worcestershire sauce, and hot sauce (if using). Stir well to combine.
Simmer: Bring the mixture back to a simmer over low heat and cook for an additional 10 minutes to allow the flavors to meld.
Cool and Store: Let the sauce cool completely before transferring it to an airtight container or bottle. Store it in the refrigerator for up to two weeks.
