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.