Preheat the grill or broiler.
In a 12 to 14-inch saute pan, heat the olive oil over medium heat and add the onion and garlic. Cook until soft and translucent, about 5 minutes. Add the peppers and potatoes and cook 5 minutes, until softened.
Add the pepper flakes, sugar, thyme, and tomato sauce, bring to a boil, lower heat and simmer 15 minutes. Season, to taste. Place the peperonata on a platter.
Grill or broil the sardines until they are crisp and the skin is slightly charred (about 2 minutes per side). While grilling the fish, divide the peperonata evenly among 4 dishes. Arrange 2 sardines atop the peperonata on each plate and serve.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic, and cook until soft and light golden brown, about 8 to 10 minutes. Add the thyme and carrot, and cook 5 minutes more, until the carrot is quite soft. Add the tomatoes and juice and bring to a boil, stirring often. Lower the heat and simmer for 30 minutes until as thick as hot cereal. Season with salt and serve. This sauce holds 1 week in the refrigerator or up to 6 months in the freezer.
Yield: 4 cups