Preheat the oven to 400°F (200°C).
In a small bowl combine the grated Parmesan and 1 teaspoon of the ranch dressing mix; set aside for sprinkling.
Make the bleu cheese ranch dip: in another bowl whisk together the mayonnaise, milk, and the remaining ranch mix, then stir in the bleu cheese crumbles; refrigerate until serving.
In a medium bowl mix the shredded chicken, shredded cheddar, and buffalo wing sauce until evenly coated.
Cut the crescent sheet into 2" x 2" squares and place them on a greased baking sheet, seam side down.
Place about 1 tablespoon of the chicken mixture in the center of each square, bring the corners together and pinch to seal tightly.
Brush each sealed crescent with the melted butter, then sprinkle the Parmesan–ranch mixture over the tops.
Bake for 15–16 minutes, or until the crescents are golden brown and cooked through.
Serve warm with the chilled bleu cheese ranch dip.