Preheat the oven to 375 degrees F. Toss the carrots with 1 tablespoon of the oil on a large baking sheet; season with salt and pepper. Roast, stirring at least once or twice, until soft, about 35 minutes.
Meanwhile, toss half the broccoli and cauliflower with the remaining tablespoon of oil and season with salt and pepper. When the carrots are about 10 minutes into cooking, add the broccoli and cauliflower and roast until tender, about 25 minutes.
Remove the cooked carrots from the baking sheet and place in food processor along with the white beans, garlic, lemon juice, cumin and paprika. Blend until smooth.
Place the roasted and raw broccoli and cauliflower on a platter and serve with the carrot hummus.
Recipe courtesy of Melissa d'Arabian