In a large skillet, heat the olive oil over medium-low heat. Add the onions and cook until softened, 4 to 5 minutes.
Cut 2 of the roasted tomatoes into thick strips and set aside. Place the rest of the tomatoes in the bowl of a food processor. Add the cooked onions, the garlic, milk and three-quarters of the basil and process until smooth. Pour into a medium saucepan set over medium-high heat. Stir in the sherry and chicken broth and bring the soup to a boil. Reduce the heat to a simmer and cook for 15 minutes more. Ladle into bowls, season to taste with salt and pepper and garnish with the strips of roasted tomatoes, shredded cheddar and the remaining basil.