In a large pot, heat 2 tbsp. olive oil over medium. Add the onion and cook, stirring occasionally, until soft, about 5 minutes. Add the carrots and garlic. Cook, stirring often, until the carrots are lightly golden, about 6 minutes. Add the stock, beans, red peppers, vinegar and salt. Simmer until the carrots are tender and the beans break down, about 20 minutes more.
Using an immersion blender or in a standard blender, puree the soup about 1 minute. Refrigerate until cold, about 2 hours. Season; stir in 2 tbsp. olive oil. Transferthe soup to a leak-proof insulated container. Serve chilled or at room temperature in cups or bowls; drizzle with the yogurt and olive oil.