Place the chickpeas in a food processor or high-speed blender along with the carrots, olive oil, salt and pepper, tahini, cumin, paprika, garlic, and lemon juice. Pulse a few times to break it all down. With the motor running, drizzle in 1/3-1/2 cup water. Continue blending, stopping every now and then to scrape the sides of the processor down before proceeding. If the mixture is overly thick, you can continue to drizzle in water by the tablespoon until it has a perfectly spreadable, but not runny, texture.