Preheat the oven to 450 degrees. Line a baking sheet with parchment paper. Put eggplant on baking sheet, drizzle with 2 tablespoons olive oil and sprinkle with 1 teaspoon salt and ½ teaspoon pepper. Toss to coat. Bake for 20-25 minutes or until the eggplant is soft and golden brown.
Place eggplant in food processor fitted with a steel blade. Add remaining ingredients and pulse until chopped. With the machine running, slowly add 1/3 cup olive oil and process until smooth. Add additional salt and pepper, if needed.