Preheat oven to 350 degrees F (175 degrees C).

Unroll crescent roll dough onto a work surface; make 4 rectangles by placing 2 dough triangles next to each other. Pinch perforations closed.

Mix cream cheese, 1 tablespoon butter, salt, black pepper, milk, and minced onion in a bowl until evenly combined; gently stir chicken into cream cheese mixture. Spoon 1/4 the chicken mixture onto each dough rectangle. Roll dough over the filling and pinch seams closed. Place onto a baking sheet. Spread about 1 1/2 teaspoons butter on each pocket and sprinkle with cracker crumbs.

Bake in the preheated oven until browned and filling is hot, 20 to 25 minutes.