1. Preheat broiler with the rack in the upper position. Cut off tops and bottoms of peppers; discard. Slice side of each pepper to open, and spread to flatten. Remove and discard ribs and seeds. Brush 1 tablespoon oil on a baking sheet. Rub peppers with oil, and flatten as much as possible. Place on sheet, skin side up. Broil until skins have blackened, about 8 minutes. Let cool. Hold peppers under running water to remove charred skins, and cut crosswise into 1/4-inch-thick strips (about 2 cups). Reduce oven temperature to 350 degrees.

2. Prepare an ice-water bath. Bring a medium pot of water to a boil. Add tomatoes, and cook until skins loosen, about 1 1/2 minutes. Using a slotted spoon, transfer to ice-water bath until cool enough to handle, about 1 minute. Peel tomatoes, and cut into quarters. Run a knife along flesh to remove seeds; discard seeds. Cut tomatoes lengthwise into 1/4-inch-thick strips.

3. Heat remaining 2 tablespoons oil in small ovenproof pot over medium-high heat. Add garlic and onion, and cook for 2 minutes; cover, and transfer pot to oven. Bake for 10 minutes. Brush down sides of pot with a wet pastry brush to prevent caramelized bits from burning. Add roasted pepper strips, cover, and bake for 20 minutes more. Brush down sides of pot again. Add thyme and tomato strips, and continue baking, uncovered, for 5 minutes. Brush down sides of pot again. Season with salt and pepper. Vegetables should be soft but not browned. Serve warm or at room temperature.