1. Heat the oven to 375°F (190°C).
2. Cut the carrot, eggplant, and red bell pepper into 1-inch chunks and spread them on a flat baking sheet lined with parchment paper. Season with salt and pepper.
3. Take the head of garlic, slice a small amount off the top so the tips of the cloves are exposed, but keep the end where the cloves connect intact. Drizzle with a little olive oil, season with salt and pepper, and wrap it in foil.
4. Roast the vegetables and the garlic for 30 minutes, or until soft. Allow them to cool.
5. Combine the roasted vegetables and garlic in a food processor with the remaining ingredients. Blend until smooth. You may need to do this in multiple batches, depending on the size of your food processor.