1. In a large nonreactive saucepan, combine vinegar, chiles, and salt. Bring to a boil over medium-high heat. Remove from heat and let cool. Transfer mixture to the jar of a blender; blend until smooth and strain.

2. Place carrots in another large saucepan; add enough water to cover. Bring to a boil over medium-high heat and immediately reduce heat to a simmer. Simmer until very tender but not overcooked, about 10 minutes. Drain and transfer carrots to the jar of blender; blend until smooth. Stir into strained chile mixture. If mixture is too spicy, add a little water to minimize the heat.

3. Use hot sauce immediately or store in a sterilized airtight container, refrigerated, for up to 1 year.