Preheat your oven to 375°F (190°C) to ensure even baking.
In a large mixing bowl, combine the cooked chopped chicken, cream cheese, ½ cup of shredded cheddar cheese, cream of chicken soup, milk, and frozen mixed vegetables. Stir until creamy.
Open the can of refrigerated crescent rolls and unroll the dough on a clean surface. Separate the dough into triangles.
Spoon a generous amount of the chicken filling onto the wider end of each crescent roll triangle. Avoid overfilling.
Starting from the wide end, roll the crescent rolls up tightly and place them seam-side down on a baking sheet lined with parchment paper.
Sprinkle the remaining ½ cup of shredded cheddar cheese over the top of each rolled-up crescent.
Bake in the preheated oven for 15-20 minutes, or until golden brown and bubbly.
Remove from the oven, let cool for a few minutes, and serve warm.