1. In a bowl, mix flour, baking powder, baking soda, and 1/2 teaspoon salt. With two knives, a pastry blender, or your fingers, cut or rub in butter until mixture resembles coarse meal.
2. With a fork, mix in parsley, chives, and tarragon. Pour in buttermilk and stir gently until mixture comes together. Scrape onto a lightly floured surface and, with lightly floured hands, knead gently just until dough forms a ball.
3. Pat dough into an even round 1/2 inch thick. Using a 3-inch round cutter or wineglass, cut out biscuits. Gather scraps, pat out again, and cut out remaining biscuits; you should have 8 total. Space evenly on a buttered 10- by 15-inch baking sheet and sprinkle evenly with remaining shredded cheese.
4. Bake in a 425° oven until biscuits are puffy and golden brown, about 15 minutes. Transfer to wire racks to cool completely.
5. In a fine strainer, rinse red onion under cold running water; let drain. In a bowl, mix mayonnaise, lemon juice, and mustard. Add shrimp, celery, the red onion, and salt and pepper to taste. Cut biscuits in half horizontally. Spoon shrimp salad onto bottom halves, then set tops in place.