Melt the butter in a large pot over low heat. When the butter begins to foam, add the onion; cook until the onion begins to turn translucent, 3 to 4 minutes. Add the chicken broth, carrots, potatoes, herbes de Provence, thyme, and bay leaf; season with salt and pepper. Raise heat to medium-high and bring to a boil; reduce heat again to low and simmer until the potatoes are tender, about 30 minutes.

Pour the soup into a blender, filling the pitcher no more than halfway. Securing the lid of the blender with a folded kitchen towel, start to blend using a few quick pulses before allowing to blend continually; puree in batches until smooth. Divide into eight soup bowls; garnish each portion with about 1/2 tablespoon heavy cream and a sprig of parsley.