Remove the shells from the shrimp. Transfer the shelled shrimp to a bowl and add the baking soda. Massage the baking soda into the shrimp and set them aside.
Pour the water and vermouth into a large skillet. Add the garlic, bay leaves, tarragon, and Old Bay, and bring the mixture up to a boil. Reduce to a simmer and cook for 15 minutes.
Take the skillet off of the heat and add the shrimp. Cover and let sit for 3 minutes. Once the shrimp turn pink, transfer them to a bowl and set them aside to cool.
Place the butter, garlic, chives, and salt in a bowl. Using a wooden spoon or a hand mixer, cream the ingredients into the butter. Transfer the butter to a ramekin and set it aside.
Coarsely chop the shrimp and place them in a bowl. Add the fennel, mayo, and lemon juice and stir to combine. Chill until ready to use.
Take the buns and slather both sides with the Garlic Chive Butter. Place the buns in a skillet and toast until golden.
Line the inside of the buns with the green leaf lettuce and spoon the shrimp mixture into the buns. Garnish with additional fennel fronds and salt and vinegar potato chips.