Preheat the oven to 400 degrees F. Cut the top off the head of garlic, exposing the cloves. Place on a sheet of foil, drizzle with olive oil and sprinkle with salt and pepper. Wrap up the garlic tightly and roast until soft, 20 to 30 minutes; let cool slightly. Squeeze out the roasted garlic.
Meanwhile, drizzle a baking sheet with 1 tablespoon olive oil. Add the carrots and rutabagas, season with salt and pepper and toss. Roast until the veggies are tender, 15 to 20 minutes.
Combine the beans, lemon zest and juice, thyme, roasted garlic and the remaining 1 1/2 tablespoons olive oil in a food processor or blender. Pulse until nice and creamy. Season with salt and pepper. If the dip is too thick, blend in some of the liquid from the beans (or use low-sodium vegetable broth). Transfer to a bowl and drizzle with olive oil. Serve with the roasted vegetable sticks and pita chips.