Preheat the oven to 450ºF. Toss the carrots with 1 tablespoon of the olive oil and 3/4 teaspoon salt. Transfer to a rimmed baking sheet and roast until tender and charred in some places, 25 to 35 minutes.

In a blender or food processor, combine the carrots, 3/4 cup water, the remaining 2 tablespoons olive oil, the lemon juice, tahini, garlic, cumin, and paprika and blend until completely smooth, stopping to scrape down the sides. Season to taste with salt, transfer to a bowl, and garnish with a drizzle of olive oil and a sprinkle of paprika.