Heat butter in a large pot. Add the shallots and toss briefly in the hot butter without browning.
Meanwhile, soak the French bread slices in the milk and let stand 10 minutes. Beat with a whisk or add to a blender in order to obtain a purée
Combine the bread puree with the stock then add this mixture to the shallots.
Simmer together 15–20 minutes.
Add Salt and pepper to taste.
Mix in sour cream and heavy cream to the soup mixture.
Add the parsley.
Return to a simmer and serve very hot.