Preheat oven to 350°F (180°C). Spray an 11 x 7-inch baking dish with cooking spray. You can also use a 9 x 13-inch dish — it will just yield a slightly thinner crust and chicken layer.
Unroll crescent roll dough and press into the bottom of the prepared dish to form a crust. Tuck the ends of the dough under as needed to fit the pan. Set aside.
In a medium bowl, stir together the chicken, ¾ cup of Alfredo sauce, and pesto. The chicken should be nicely coated in sauce, so add a little bit more Alfredo if the mixture seems dry. You just don’t want too much sauce, which can make the crust soggy. Taste and season with salt and pepper, if desired.
Spread chicken mixture in an even layer over the crescent roll dough. Sprinkle shredded cheese on top.
Bake for 20-25 minutes, or until the crust is a deep golden brown. Cut into squares, garnish, and serve.