Bring a large pot of salted water to a boil. Reduce heat to medium-high, and add shrimp. Poach until opaque throughout, 3 to 4 minutes (the water should never return to a boil). Drain shrimp, and spread on baking sheet; let cool. When no longer steaming, refrigerate to cool completely, about 40 minutes. Peel and devein shrimp. Shrimp can be refrigerated up to 1 day.
Mix together chopped scallions, tarragon, lemon zest and juice, and mayonnaise. Stir in shrimp, sliced celery, and 1 teaspoon salt. Refrigerate until cold, at least 30 minutes and up to 4 hours.
Preheat a griddle or grill to medium-high heat. Brush butter on inside surface of each bun. Place buns on griddle or grill, buttered sides down, and toast until golden brown or lightly charred.
Divide shrimp mixture among buns. Top with celery leaves and scallion greens.