With a heart-shaped cookie cutter or a knife, cut heart shapes (3 inches wide or smaller) out of bread. Lay cutouts on a baking sheet and brush tops with about 2 teaspoons oil. Sprinkle evenly with 1/4 teaspoon basil. Bake in a 350° oven until golden and crisp, about 15 minutes for a 3-inch-wide heart.
Meanwhile, in a 2- to 3-quart pan, cook shallots, stirring often, in remaining 1 teaspoon oil over medium-high heat until shallots are translucent, about 3 minutes. Add broth, red peppers, tomatoes and their juice, and remaining 1/2 teaspoon basil. Bring to a boil over high heat; cover and simmer over low heat 5 to 10 minutes.
With a slotted spoon, ladle peppers, tomatoes, and shallots into a blender or food processor; whirl until smooth. Return purée to pan; stir into liquid. Add salt, pepper, and sugar to taste. Ladle soup into bowls. Spoon dollops of sour cream decoratively over soup; swirl the tip of a knife through sour cream. Immediately before serving, set heart-shaped croutons on top.