For the lemon aioli: In a food processor, combine the egg yolks and whole egg and slowly alternate drizzling in the olive oil and lemon juice while processing. Add the lemon zest and pulse until fully incorporated. Season with salt and pepper.
For the shrimp and poaching liquid: Combine 12 cups water, the wine, Old Bay, salt, bay leaves, garlic and lemon in a medium, high-sided pot. Bring to a low boil and cook for 10 minutes to allow the flavors to marry.
Fill a medium mixing bowl with ice and set aside.
Carefully add the shrimp to the simmering poaching liquid and cook until bright pink and beginning to curl, about 5 minutes. Transfer half of the poaching liquid to the bowl of ice. Drain the shrimp in a strainer and add it to the iced poaching liquid to cool. Remove the shells and dice the shrimp into medium-sized pieces.
For the salad: In a mixing bowl, stir together the tarragon, celery, lemon zest and juice, 1 cup of the lemon aioli and the shrimp. Season with salt and pepper. Serve.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.