This smoky paste is a wonderful addition to jazz up any meal.
Place árbol, guajillo, and ancho chiles in a large heatproof measuring glass. Pour boiling water over them to submerge, cover with plastic wrap, and let sit until chiles are very pliable and cool enough to handle, 15–20 minutes.
Drain then remove stems and seeds and discard.
Toast cumin and coriander in a dry small skillet over medium-low heat, tossing constantly, until very fragrant, about 3 minutes. Transfer to a food processor, add garlic and pulse until a paste is formed.
Add chiles and pulse until chiles form a coarse paste. Add lemon juice, vinegar, tomato paste, paprika, and salt and process until mostly smooth with some texture. Stream in ½ cup oil with the food processor still running. Process until oil is incorporated.