Step 1

Place árbol, guajillo, and ancho chiles in a large heatproof measuring glass. Pour boiling water over to submerge, cover with plastic wrap, and let sit until chiles are very pliable and cool enough to handle, 15–20 minutes. Drain; remove stems and seeds and discard (wear gloves for this part if you have them).

Step 2

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 spices are broken up and garlic forms a paste. Add chiles and pulse until chiles form a coarse paste. Add lemon juice, vinegar, tomato paste, paprika, and salt and process until mostly smooth but mixture still has a little texture. With the motor running, stream in ½ cup oil. Process until oil is incorporated.

Step 3

Transfer harissa to a bowl. Pour remaining ¼ cup oil over top.

Step 4

Do Ahead: Harissa can be made 1 month ahead. Cover and chill.