Add 2 tbsp butter and garlic to a large skillet over low heat. Cook on very low to let the garlic infuse into the butter, about 2 minutes.
Pat shrimp dry with a paper towel and season with salt and pepper. Add shrimp to skillet and cook, stirring occasionally until pink. Keep the heat on low, so the shrimp cook gently in the butter. Once cooked, remove from heat, and set aside to cool.
In a medium bowl, add the mayo, mustard, Calabrian paste, celery, chives, lemon zest and juice, and season with salt and pepper.
Cut the shrimp into bite sized pieces and add into bowl. Toss to combine. Place in the fridge to keep cold.
Melt remaining butter in the same skillet over medium heat. Add the buns and toast on both sides until golden. Turn off the heat and set aside.
Assemble the rolls: add the shrimp salad to the buns and top with fresh cilantro and celery leaves. Serve.