In food processor, combine basil, garlic, pinenuts, salt and pepper until well combined. Add half oil and puree. Add remaining oil and cheese until blended. Brush tomato and eggplant slices with oil and roast in a preheated oven for five minutes, turning once. Lightly brush muffins with pesto and toast under broiler. Poach eggs.
To assemble, put muffin on plate, stack tomato and eggplant on top of each serving. Carefully place egg on top and drizzle with pesto. Serves four.