In a 3-quart saucepan heat olive oil. Add carrots and onions and cook until soft. Add peppers and cook 2 minutes more. Add potatoes and stock and bring to a boil. Reduce heat and simmer until potatoes are cooked through and starting to fall apart, about 25 minutes. Season with salt and pepper, to taste.
Use a stick blender, food processor or blender to puree soup. If necessary, return to pot and reheat. Garnish each portion with 1 teaspoon of pesto. Serve immediately.