Start the vegetables: Heat the oven to 425°F. Set a rack in the middle of the oven and place a large Dutch oven or soup pot on the stove.

Start the vegetables: Put the carrots, onion, and garlic on a large sheet pan.

Start the vegetables: Drizzle the vegetables with the olive oil. Sprinkle on 1 teaspoon of the cumin, the smoked paprika, and 1 teaspoon of the salt, then toss until everything is coated.

Start the vegetables: Spread the vegetables into a single layer on the sheet pan so they roast instead of steam.

Start the vegetables: Roast for 25 to 30 minutes, stirring once halfway through, until the carrots are tender and the edges are browned.

Simmer the lentils: While the vegetables roast, put the lentils and the vegetable broth into the Dutch oven.

Simmer the lentils: Bring the pot to a boil over high heat.

Simmer the lentils: Lower the heat to medium-low so the broth bubbles gently. Simmer for 20 to 25 minutes, until the lentils are mostly tender but still hold their shape.

Blend the soup base: Take the sheet pan out of the oven. Let the vegetables sit for 2 minutes so they are easier to handle.

Blend the soup base: Transfer the roasted carrots, onion, and garlic to a blender. Ladle 1 cup of the hot broth from the pot into the blender.

Blend the soup base: Blend until very smooth. Leave the small cap in the blender lid slightly open and cover it with a folded kitchen towel so steam can escape safely.

Finish the soup: Pour the carrot mixture back into the Dutch oven with the lentils.