Preheat oven to 415 degrees F.
Lightly oil a large (16 by 30-inch) cookie sheet, or 2 smaller (11 by 17-inch) sheets.
Using a rolling pin or your hands, flatten dough to fit in your cookie sheet. Using finger tips, poke indentations across entire surface. Spread a thin layer of tomato sauce over surface. Sprinkle with olives. Lay anchovy fillets out into a pattern. Sprinkle with onions, capers, and drizzle with extra virgin olive oil. Place in oven and bake 15 to 20 minutes, until golden brown on bottom. Remove and serve hot or cold.
Saute the onion and garlic in the olive oil over medium heat until translucent, but not brown (about 10 minutes). Add the thyme and carrot and cook 5 minutes more. Add the tomatoes. Bring to a boil, lower the heat to just bubbling, stirring occasionally for 30 minutes. Season with salt to taste. Serve immediately, or set aside for further use. The sauce may be refrigerated for up to one week or frozen for up to 6 months.