Preheat oven to 400 degrees F. Puncture the eggplant all around with a sharp knife. Place on a baking sheet or shallow baking dish and bake about 1 1/2 hours until it is very soft. Meanwhile soak anchovy fillets in cold water for about 10 minutes. Pat dry and smash with a fork. Place anchovy in a large bowl; add garlic, shallot, capers and pepper. Add a tablespoon olive oil and mix. Set aside. Once eggplant is done, allow to rest until is cool enough to handle. Cut open and scoop out the pulp into a large strainer. Scrape the inside of the skin with a spoon to remove all the pulp. Press pulp into strainer to remove as much moisture as you can. Let drain about 10 minutes, then transfer to a cutting board; chop fine. Place chopped eggplant in the bowl with the other ingredients and mix well. Add remaining 3 tablespoons of olive oil and mix until smooth. Add lemon juice to taste and salt to taste. Spoon into a serving bowl and sprinkle with chopped parsley. Place egg in a small serving bowl; red onion in another small bowl; capers in another bowl; and Greek yogurt in still another small bowl. Serve with toast or pita wedges.