Soak lettuce leaves for about 10 minutes in ice water to reduce bitterness. Wrap in damp paper towel to keep moist until ready to serve.
In large saute pan, heat 2 tablespoons olive oil over medium-high heat until hot. Add the garlic and saute briefly until brown. Add the onion and brown lightly, about 3 minutes. Reduce the heat to medium, add a pinch each of salt and pepper (go easy on the salt because the anchovies will add that extra bit of saltiness). Continue to cook until the onion is well browned, about 5 minutes. Add the anchovies and cook and stir until they melt into the onion. Add the chili flakes, then the caper juice and stand back to avoid getting splattered. Stir and scrape all around the pan. Add 1/4 cup of the vinegar, return the heat to high, and boil until reduced and thick, 1 to 2 minutes.
In a separate pan, heat 2 tablespoons of the olive oil in a large saute pan over medium-high heat until hot. Add the eggplant and saute until browned and cooked through, about 6 minutes. Saute only a small bunch at a time, to avoid letting the eggplant boil in its own juices. If the pan gets too dry, add more olive oil as the cooking progresses - if you add too much olive oil early in the process, the eggplant will absorb all of it and still need more. Make sure to scrape the bottom of the pan well so nothing burns. Season with salt and pepper. Scrape into a bowl.
Add the garlic-anchovy mixture to the eggplant with the capers and remaining vinegar. Stir well, then scrape into a bowl. Stir in the roasted peppers and parsley and taste again for seasoning. Let cool to room temperature before serving.
When ready to assemble, place 1 to 2 tablespoons of caponata in chilled lettuce cups. Wrap into ball and enjoy.
Brush peppers with olive oil (this carries the heat into crevices, helping the skin to blister more evenly). Roast the peppers whole under a broiler or on the stovetop, or grill, turning occasionally until the skins blister and char all over.
Place in paper bag, and let steam to loosen the skins, for about 15 minutes. Working over the bowl to catch any juices, peel off the skins. Seed the peppers, then slice into long strips and place in a clean bowl. Pour the juices left in the steaming bowl over the peppers and refrigerate for up to several days.
*Never rinse a roasted pepper under running water in the sink as you peel it - you'll be rinsing the flavor away! You want that smoky, charred character to stay in the peppers. If you plan to serve the caponata as part of an elegant appetizer, use a sharp chef's knife to cut the eggplant into 1/4-inch dice. If your style is more casual, you may dice them as large as 3/4 inch. The caponata also makes a wonderful sandwich filling or stuffing a chicken paillard.