Preheat oven to 350°F. Place butter and cream cheese in a medium bowl to soften.
Stir mayonnaise into butter and cream cheese mixture until blended. Fold in chicken. Set aside.
Combine cream of chicken soup and milk in another medium bowl. Pour 1/2 cup the soup mixture at the bottom of a 13×9-inch baking dish.
Unroll and separate crescent rolls on a flat work surface or a large cutting board. Place 1/3 cup chicken mixture on the wide end of each crescent roll, then roll it over the filling; place rolls in the baking dish, seam side down, leaving some room in between each roll. Repeat with the remaining rolls and the chicken mixture.
Stir the prepared vegetables in the remaining soup mixture; pour over rolls and top with cheddar cheese. Cover with foil and bake for 25 minutes.
Remove foil. Bake for 10 more minutes, uncovered, or until the dish is bubbly. Serve.
You could also use an 8×8-inch baking dish as pictured in this recipe. However, it’d be pretty full. It’s recommended to use a bigger baking dish and keep some distance between each crescent roll.
You can assemble the casserole the night before and store it in the fridge until ready to bake.