Place the dried chiles in a heat-safe bowl and cover with hot water. Let them soak for 30 minutes until soft. Drain the water and remove stems and seeds.

In a small dry skillet, toast the caraway seeds over medium heat until fragrant. Then, if needed, use a spice grinder to crush them into a fine powder.

In a food processor, combine the rehydrated chiles, roasted red peppers, tomato paste, garlic, toasted caraway, ground coriander, cumin, smoked paprika, cayenne pepper, and a pinch of black pepper and kosher salt. Add lemon juice.

With the processor running, slowly drizzle in the olive oil until you reach a smooth, thick paste. Taste and adjust seasonings if needed. Spoon the paste into a jar and top with a thin layer of extra olive oil. Refrigerate to let flavors deepen.