Combine shrimp, mayonnaise, and fennel in a medium bowl.
Cut a V-shaped opening in the top of a long roll. Butter each roll. Place the 6 rolls, buttered side up, on a baking sheet. Place under the broiler and cook until just golden.
Place a layer of avocado on the rolls and top with shrimp salad. Serve immediately.
Bring a large saucepot of water to just below a simmer. Season the water heavily with salt and drop in the peppercorns; the water should taste salty like seawater. Immerse the shrimp into the hot water. Simmer for 1 to 2 minutes or until the shrimp are opaque throughout. Remove from water and chill immediately until completely cool.
Whisk the egg yolks, Dijon mustard, and lemon juice in a small stainless-steel bowl. Add the vegetable oil in a very, very slow stream, whisking to emulsify. Stir in the salt and tarragon.
Keep avocados from browning by keeping plastic wrap directly on the slices for up to 30 minutes before using
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