1. Heat oil in a saucepan over medium-high. Add onion, garlic, and 1 teaspoon salt; cook until onion is translucent, about 3 minutes. Stir in ketchup, mangoes, sugar, vinegar, and 3/4 cup water; bring to a boil. Reduce heat to a simmer and cook, partially covered and stirring occasionally, until slightly reduced and mangoes are very soft, about 30 minutes. Let cool 5 minutes.

2. Puree mango mixture, chile, and Worcestershire in a blender until smooth. Season with salt and more vinegar; let cool completely. Sauce can be refrigerated in an airtight container up to 1 week, or frozen up to 3 months.