Preheat oven to 375°. Line a rimmed baking sheet with parchment paper.
On a lightly floured surface, unfold puff pastry sheets. Using a 2¼-inch round cutter, cut 12 circles from each pastry sheet. Place 12 circles on prepared pan. Brush with egg. Using a 1¼-inch round cutter, cut a circle in center from remaining 12 circles. Place on top of egg-washed rounds.
Bake until golden brown, 10 to 15 minutes. Let cool completely.
In a large bowl, whisk together mustard, sugar, salt, and paprika. Whisk in oil in a slow, stream until fully combined. Add shrimp, green onion, celery, parsley, and hot sauce, stirring until coated and well combined. Spoon shrimp mixture into pastry cups. Garnish with celery leaves and parsley leaves, if desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/shrimp-remoulade-cups/