Preheat the oven to 375°F.
Cut the eggplant into thick slices, then quarter each slice. Transfer the eggplant pieces to a large bowl.
Cut the carrot into thick slices, then cut the bell pepper into about 8 pieces. Add everything to the bowl with the eggplant.
Add 1 tablespoon of olive oil to the bowl and sprinkle with salt and pepper. Toss until everything is well-coated, then transfer to a baking sheet.
Keeping the head of garlic intact, remove the loose outer skin. Slice off the top to expose the cloves, then place the head, cut-side up, on a piece of foil.
Drizzle the garlic with the remaining ½ tablespoon of olive oil, then wrap it in the foil and add it to the baking sheet.
Place the baking sheet in the oven and roast for 30 minutes or until everything has softened, then remove from the oven and allow to cool.
In a food processor, combine the roasted eggplant, carrot, and bell pepper along with the chickpeas, walnuts, sun-dried tomatoes, 2 tablespoons of oil from the jar of sun-dried tomatoes, ¼ teaspoon of salt, and a few grinds of black pepper.
Squeeze each clove of garlic out of the skin, then add to the food processor.
Purée the ingredients, stopping the processor and scraping down the sides a couple of times, until the paté is smooth.