Soften the chilies: Remove stems and seeds from the dried chilies. Place them in a bowl of hot water and soak for 30 minutes until soft. Drain well.
Blend the paste: In a food processor (or mortar and pestle for traditional method), combine softened chilies, garlic, cumin, coriander, caraway, and salt. Blend until smooth.
Add olive oil: Drizzle in olive oil while blending to form a thick, rich paste. Add lemon juice if desired for extra freshness.
Store: Transfer to a sterilized jar, smoothing the top. Pour a thin layer of olive oil over the surface to preserve. Store in the fridge for up to 3 weeks.