Step 1: Soak the Dried Chiles. Place dried New Mexico or Guajillo chilies in a heat-safe bowl and cover completely with hot water. Soak for 30 minutes until softened. Drain, then remove stems and seeds.
Step 2: Combine the Ingredients. Add soaked chilies, roasted red peppers, tomato paste, garlic cloves, caraway seeds, coriander, cumin, smoked paprika, cayenne pepper, lemon juice, and salt to a food processor.
Step 3: Blend Into Paste. Turn on the food processor and slowly add olive oil through the opening while blending. Scrape down the sides and continue blending until the mixture becomes a thick, slightly chunky paste. Adjust salt or cayenne to taste.
Step 4: Store the Harissa. Transfer the finished harissa paste into a clean glass jar. Smooth the surface and pour a thin layer of extra virgin olive oil on top to protect freshness. Seal tightly and refrigerate.
