Heat 2 tablespoons of the olive oil in a large sauti pan over medium-high heat until hot. Add the eggplant and sauti until browned and cooked through, about 6 minutes. Add more olive oil as the cooking progresses if the pan becomes too dry. If you add more early on, 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.

In the same pan, heat another 2 tablespoons olive oil over medium-high heat until hot. Add the garlic and sauti briefly until brown. Add the onion and cook until beginning to brown, about 3 minutes. Reduce the heat to medium, and add the thyme and a pinch each of salt and pepper. Go easy on the salt because of the anchovies. 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 caper juice and stand back to avoid getting splattered. Stir and scrape all around the pan. Add the vinegar, return the heat to high, and boil until reduced and thick, 1 to 2 minutes. Add the eggplant and capers, 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. Serve with crackers or bruschetta.