Place 4 ounces cream cheese in a medium bowl and let sit at room temperature until softened, at least 30 minutes.

Arrange a rack in the middle of the oven and heat the oven to 375ºF. Line a rimmed baking sheet with parchment paper. Meanwhile, make the filling.

Shred 2 ounces sharp cheddar cheese on the large holes of a box grater (about ½ cup). Trim and thinly slice 2 medium scallions (about o¼ cup). Finely chop cooked chicken until you have ½ cup.

Beat the cream cheese with a fork to soften. Add ¼ cup of the cheese, ¼ cup of the dressing, and ¼ cup hot sauce, and mix until combined. Add the chicken and scallions and stir to combine.

Open 1 can crescent roll dough and carefully unroll onto a cutting board with a longer side closer to you. Firmly press the perforations together to seal, then press out into a 12-by-8-inch rectangle. With a sharp knife or pizza cutter, cut the dough into 12 rectangles (3 across and 4 down).

Divide the chicken mixture onto the center of each rectangle (about 1 ½ tablespoons each). Seal the puffs one at a time: Carefully stretch out and bring the 4 corners up to meet over the center of the filling, and pinch where they meet to seal. Press down slightly, allowing the filling to be visible. Place on the prepared baking sheet spaced at least 1 ½-inches apart.

Brush the tops of the puffs with the remaining 1 ½ tablespoons dressing. Sprinkle with the remaining ¼ cup cheese.

Bake for 7 minutes. Rotate the baking sheet and bake until the pastry is golden-brown and the filling is bubbly, 7 to 9 minutes more. Meanwhile, coarsely chop ¼ cup celery leaves, if using.

When the puffs are ready, transfer to a wire rack and let cool 5 minutes. Transfer to a platter and garnish with the celery leaves if desired. Serve warm with carrot and celery sticks, plus more dressing for dipping.