Preheat the oven to 350°F. Spray a 9-by-13-inch baking dish with cooking spray.
In a small saucepan, combine the milk, cream of chicken soup, Italian seasoning, and ½ cup of the cheddar over medium heat. Bring to a gentle simmer, stirring frequently, until the cheese is melted, 2 to 3 minutes. Remove from the heat and pour into the prepared baking dish.
In a large bowl, mix the cream cheese with an electric hand mixer or sturdy spatula until smooth. Stir in the garlic powder, pepper, salt, and a few dashes of hot sauce, if using. Fold in the chicken, jalapeño, 2 of the sliced green onions, and the remaining 1 cup cheddar.
Working swiftly to keep the dough cold, unroll the crescent dough and separate the perforated dough into 16 triangles. Place 2 packed tablespoons of filling (a cookie scoop helps a lot) along the short edge of a triangle and roll up the filling toward the pointed end. Pinch the sides to seal. Repeat with the remaining dough and filling. Nestle the roll-ups into the sauce in the baking dish.
Bake until golden and bubbly, 35 to 40 minutes. Let sit at least 5 minutes before sprinkling with the remaining 2 sliced green onions and serving.