Begin by whisking together mayonnaise, lemon juice, and hot sauce in a large bowl until smooth. Fold in chopped scallions, diced celery, and minced chives. Chill in the refrigerator for at least 30 minutes.

Preheat your grill to medium-high heat, about 400°F (200°C). Pat shrimp dry and toss with olive oil and kosher salt. Grill shrimp for 2-3 minutes on each side until pink and opaque. Remove and let cool slightly before chopping.

Reduce grill heat to low. Cut brioche buns in half and toast them cut-side down on the grill for approximately 30 seconds to 1 minute until golden brown.

Carefully fold chopped shrimp into the chilled mayonnaise mixture until evenly coated. Spoon the mixture into the toasted brioche buns, and garnish with minced chives, sliced scallions, and a sprinkle of flaky sea salt.