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For the harissa relish, place cumin and caraway seeds in small frying pan over medium heat. Toast, shaking pan occasionally, until lightly browned and fragrant, 2 to 3 minutes. Remove from heat and add chili flakes. Toast for 10 seconds. Transfer to plate to cool.
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In a spice grinder or with a mortar and pestle, coarsely grind cooled spices. Add to bowl with piquillo peppers, garlic, olive oil and salt. Mix. Transfer to airtight container. (Relish will keep in fridge up to 1 week. Bring to room temperature before serving.)
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For the soup, heat oil in a large pot over medium heat. Add onions. Cook, stirring occasionally, until soft and just starting to brown, 8 to 10 minutes. Add garlic. Cook 1 minute. Add spices. Cook 30 seconds. Add carrots and stock. Raise heat to high. When it comes to a boil, reduce to a simmer and cook until carrots are soft, about 20 minutes. Working in batches, purée soup in a blender until smooth. Transfer to a clean pot. Stir in lemon juice. Season with salt and pepper. Keep warm over a low heat.