Preheat the oven to 400 degrees F (200 degrees C).
Melt butter in a nonstick skillet over medium heat. Pour in beaten eggs; cook in hot butter to desired degree of doneness, stirring constantly. Remove from heat.
Unroll crescent dough and place rolls on an ungreased 12-inch pizza pan with points facing the center. Press seams together and press up sides of the pan to form a crust.
Prepare Hollandaise sauce according to the package directions using 2/3 cup milk and 1/4 cup butter. Pour sauce evenly over crescent roll crust. Spread scrambled eggs evenly over sauce, then top with diced ham. Sprinkle with cheese.
Bake in the preheated oven until bottom of crust is lightly browned, about 30 minutes.