Remove the stems and most of the seeds from the dried chiles.
Cover the chiles with very hot water and soak for 20–30 minutes until completely softened.
Peel the garlic cloves.
Juice the lemon.
Measure all remaining ingredients.
Drain the softened chiles, reserving ¼ cup of the soaking liquid.
Toast the caraway, coriander, and cumin seeds in a dry skillet over medium heat for 1–2 minutes until fragrant.
Grind the toasted spices into a fine powder using a spice grinder or mortar and pestle.
Preparation
Add the softened chiles, garlic, toasted ground spices, smoked paprika, tomato paste (if using), kosher salt, and lemon juice to the bowl of a food processor.
Process until finely chopped.
With the processor running, slowly drizzle in the olive oil until incorporated.
Add 2–4 tablespoons of the reserved chile soaking liquid as needed until the harissa reaches a thick, spreadable consistency.
Taste and adjust seasoning with additional salt, lemon juice, or olive oil if desired.
Transfer the harissa to a small saucepan and cook over low heat for 3–5 minutes, stirring frequently. This step slightly mellows the garlic and allows the flavors to blend together.
Allow the harissa to cool completely.
Transfer to a clean glass jar and smooth the surface.
Pour a thin layer (about 1 tablespoon) of olive oil over the top before sealing the jar to help preserve freshness.