Place the guajillo and arbol chiles in a heatproof bowl. Pour the boiling water over them and press down to submerge. Let soak for 15 minutes until completely softened and pliable. Reserve 1/2 cup of the soaking liquid before draining.

While chiles soak, heat a small dry skillet over medium-low heat. Add the cumin, coriander, and caraway seeds. Toast for 2-3 minutes, shaking the pan frequently, until fragrant and just starting to darken. Immediately transfer to a plate to cool, then grind the caraway seeds.

Drain the soaked chiles and transfer to a food processor. Add the garlic, tomato paste, toasted cumin, coriander, ground caraway, smoked paprika, olive oil, lemon juice, and salt. Pulse until a coarse paste forms, scraping down the sides as needed.

With the processor running, drizzle in the reserved soaking liquid one tablespoon at a time until the harissa reaches a thick, spreadable consistency similar to tomato paste. You may not need all the liquid.

Taste and adjust salt or lemon juice as needed. Transfer to a clean glass jar, smooth the top, and cover with a thin layer of olive oil to preserve freshness. Seal and refrigerate. The harissa improves after 24 hours and keeps for up to 3 weeks.