Wear gloves if handling very hot chiles. Rinse chiles, remove stems, and halve. For milder heat remove seeds and membranes; for hotter sauce leave some or all in. Roughly chop so they fit into a blender.

Prep Vegetables

Peel and chop carrots, roughly chop onion, and peel garlic cloves so they are ready to cook.

Cook

Sauté Aromatics

Heat olive oil in a small saucepan over medium heat. Add chopped onion and carrots and sauté for 4–5 minutes until softened. Add garlic and cook 30–60 seconds until fragrant, stirring so garlic doesn't burn.

Simmer with Vinegar

Add the chopped chiles to the pan, then pour in the distilled white vinegar and water. Bring mixture to a gentle simmer, reduce heat to medium-low, and simmer uncovered for 8–10 minutes until chiles and carrots are very soft and fragrant. Stir occasionally. Add kosher salt, sugar (or honey), and black pepper about halfway through cooking so flavors meld.

Blend & Finish

Blend

Carefully transfer the hot mixture to a blender (or use an immersion blender in the pot). Blend on high until completely smooth, about 1–2 minutes. If mixture is too thick, add up to 2 tablespoons of water (or vinegar) to reach desired consistency.

Taste & Adjust

Stir in optional smoked paprika and lime juice if using. Taste and adjust salt, sugar, or vinegar balance to your preference. If too acidic, add a pinch more sugar; if too thick, thin with vinegar or water; if too mild, add a few more chiles and blend again.

Cool & Store

Allow sauce to cool to room temperature, then transfer to a clean glass bottle or jar. For best flavor rest in the refrigerator at least 24 hours before using to let flavors meld. Stores refrigerated for 2–4 weeks; for longer storage, process in a water bath canner following safe canning guidelines or freeze in portions.