Sauté the vegetables: In a medium saucepan, heat the vegetable oil over medium heat. Add the chopped onion, carrot, celery, and garlic. Sauté for 5–7 minutes until the vegetables soften and become fragrant.
Add liquids and seasonings: Pour in the water and vinegar, then add the brown sugar, salt, cumin, mustard, black pepper, turmeric, Worcestershire sauce, and tamarind paste if using. Stir to combine.
Simmer the mixture: Bring the sauce to a gentle boil, then reduce the heat and let it simmer uncovered for 15–20 minutes, stirring occasionally, until the vegetables are tender and the flavors meld together.
Blend until smooth: Remove from heat and let the mixture cool slightly. Transfer to a blender or food processor and blend until completely smooth. If desired, strain the sauce through a fine mesh strainer for a silky texture.
Taste and adjust: Taste your sauce ; you can add more vinegar for tanginess, sugar for sweetness, or salt to enhance flavor.
Store and serve: Pour the finished Salsa Lizano into a clean glass bottle or jar. Once cooled, seal tightly and refrigerate. The sauce will keep for up to one month and tastes even better after a day or two as the flavors deepen.