Combine soup, 3/4 cup cheese, 1/2 cup milk and 1 tablespoon fresh basil. Mix together and drizzle 1/2 cup of mixture in the bottom of a sprayed 9x13-inch baking pan.
In a bowl combine cream cheese and butter until smooth. Add garlic powder, onion, chicken, green chilies, 3/4 cup cheese, remaining basil and mix well Season with salt and pepper.
On a counter lightly sprayed with non-stick cooking spray, press each dinner roll into a 5-inch circle. Divide filling equally between the 12 circles. Pull dough up around filling and pinch together to seal. Place each roll into the baking pan pinched sides down. Pour remaining sauce on top of the rolls. Sprinkle with remaining cheese. Bake at 350°F 35 minutes. Cover with foil the last 5 minutes if necessary to prevent over browning.