Preheat broiler. Place peppers in oven and broil, turning occasionally, until blackened on all sides. Remove peppers from broiler, and immediately place in a paper bag and close. Set aside 15 minutes to sweat. Remove peppers from bag and slip off skins. Remove and discard seeds and core. Cut peppers into thin strips.
Heat a large saucepan of lightly salted water to boiling. Trim stem ends from beans. Drop beans into boiling water and cook, uncovered, 8 to 10 minutes, or until tender-crisp. Remove from heat, drain, and rinse beans with cold water to stop cooking.
Combine beans and peppers, and arrange on large platter. Sprinkle with salt, pepper, and parsley, and drizzle with olive oil. (Can be made up to 1 day ahead. Cover and refrigerate.