Put dried chiles (ancho and guajillo, or whatever you're using) in a medium bowl. Cover with boiling water and let sit until softened. Toast caraway, coriander and cumin in a skillet over medium heat until fragrant. Transfer spices to a grinder with dried mint and grind until fine.
Drain chiles and transfer to bowl of food processor. Add ground spices, red pepper, chipotle peppers, garlic, and lemon juice. Turn on food processor. Stream in oil until the mixture is smooth and the consistency of tomato paste. Season with salt to taste.
Transfer to a clean decorative jar and top with enough olive oil to cover. Harissa paste will keep in the refrigerator for 1 month.