Melt the butter in a saucepan over medium-low heat. Add the caraway seeds and cook until fragrant, about 1 minute. Add the mushrooms and cook, stirring, until they begin to wilt, about 5 minutes. Add 1/4 teaspoon salt, and pepper to taste. Add the carrots and broth, cover and bring to a simmer. Uncover and cook until the carrots are tender, 10 to 12 minutes. Season with salt and pepper.
Meanwhile, combine the onion, vinegar and a pinch of salt in a bowl and let marinate while the soup simmers. Toast the bread.
Divide the soup among bowls and top with sour cream and the marinated onion. Serve with the toast.