Preheat oven to 450°.
Pierce eggplants several times with a fork; place on a foil-lined baking sheet. Bake for 45 minutes or until blackened, turning frequently. Cool slightly; peel. Drain eggplant pulp in a colander for 5 minutes; chop.
Combine tomato paste and next 5 ingredients (through ground red pepper) in a small bowl, stirring until smooth.
Heat oil in a large nonstick skillet over medium-low heat. Add onion and garlic; cook 6 minutes or until tender, stirring occasionally. Stir in eggplant, tomato paste mixture, bell peppers, and anchovies; cook 10 minutes. Remove from heat; stir in parsley. Spoon mixture into a medium bowl. Cover and chill.