Heat a 3 1/2-quart saucepan over medium-high heat. Add the olive oil and heat another 30 seconds. To the hot pan, add the shallots and fennel. Sweat, stirring often with a wooden spoon, until fragrant and beginning to soften, 2 minutes. Add the garlic and 1/4 teaspoon salt and cook another 2 minutes. Add the mussels and stir gently once or twice in order to coat in the oil. Add the beer and stir one more time. Cover with a tight-fitting lid and cook until the mussels have opened, about 4 minutes, stirring halfway through. Discard any unopened mussels. Stir in the butter and tarragon and season with 1/4 teaspoon black pepper. Serve with slices of crusty bread to dip in the sauce.
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