Spray the bottom and sides of an 8 x 12-inch baking dish with cooking spray.
Allow the dinner rolls to thaw on the counter for 20-30 minutes. Arrange on the bottom of the baking dish.
Sprinkle the cubed ham over the dough quarters and sprinkle with 1/2 of the shredded cheese.
In a medium size mixing bowl whisk together the eggs, half & half, garlic salt, black pepper and ground mustard. Ur a large spatula to mix in the grated Parmesan cheese and sliced green onions.
Pour the custard over the rolls. Cover with plastic wrap and refrigerate overnight.
To bake, preheat the oven to 350°F. Remove the plastic wrap and sprinkle the remaining shredded cheese on top. Bake for 40 minutes then lay a piece of foil on top. Continue to bake for an additional 15-20 minutes or until the eggs are set.
Rest for 10 minutes before serving..