1. Put chiles into a medium bowl, cover with boiling water, and let sit until softened, about 20 minutes. Heat caraway, coriander, and cumin in an 8" skillet over medium heat. Toast spices, swirling skillet constantly, until very fragrant, about 4 minutes. Transfer spices to a grinder with the mint and grind to a fine powder. Set aside.
2. Drain chiles and transfer to the bowl of a food processor with the ground spices, olive oil, salt, garlic, and lemon juice. Purée, stopping occasionally to scrape down the sides of the bowl, until the paste is very smooth, about 2 minutes. Transfer to a sterilized 1-pint glass jar and fill with oil until ingredients are submerged by 1⁄2". Refrigerate, topping off with more oil after each use. Paste will keep for up to 3 weeks.

Makes 1 cup.