Place the first 4 ingredients in a pot and bring to a boil over medium-high heat. Boil 1 minute. Add the mussels, cover and cook until they just open, about 2 to 3 minutes. Remove from the heat. With tongs, lift the mussels out of the pot, allowing any liquid inside the shells to drip back into the pot. Set mussels on a plate to cool. Reserve the liquid in the pot.
Melt the butter in a second pot set over medium heat. Add the flour and mix until well combined. While steadily whisking, slowly pour in the stock. Strain and whisk the mussel cooking liquid into the pot. Add the tarragon and bring the bisque to a simmer. Simmer 5 minutes.
While the bisque simmers, remove the meat from 24 of the mussels and divide them among 4 shallow soup bowls. Reserve the 4 mussels in the shell for garnish.
When the bisque has simmered 5 minutes, stir in the cream. Taste the bisque and season with white pepper and salt, if necessary. Ladle into the bowls. Set a mussel in the shell in the centre of each bowl and serve.
Note: Discard any mussels that do not close when tapped before cooking, or do not open after cooking. Both are signs the mussel was dead prior to cooking and should not be eaten.