Steam the eggplants and garlic until each is soft, about 20 to 40 minutes depending on size. When cooked and cool enough to handle, peel the eggplant and garlic. Cut the eggplant flesh into cubes.
Place the eggplant, garlic, olives, anchovy fillets, salt, and both peppers in a food processor. Purée. Add the egg yolk and mustard and pulse to mix. While the processor is running, incorporate the oil a little at a time.