Throw out any mussels with cracked shells or that did not close when you scrubbed them.
Toast the fennel seeds in a pot that is just big enough to hold the mussels.
Heat the butter over medium heat in a pot just large enough to hold the mussels. Add butter. Sauté the shallots and garlic for 4 to 5 minutes. Add half the tarragon, the mussels and the aquavit. Increase the heat to medium-high. Cover and let steam for 6 to 7 minutes, until the mussels have opened. With a slotted spoon, transfer the mussels to a large serving bowl; discard any that did not open.
Cook the juices over medium-high heat for 3 minutes, until slightly reduced. Pour the cooking juices over the mussels, sprinkle with the rest of the tarragon, and serve.