Heat oven to 375°F. Grease 13x9-inch (3-quart) glass baking dish with shortening, or spray with cooking spray.
Separate dough from both cans into 16 rolls; return icing to refrigerator. Arrange rolls as evenly as possible in baking dish. Bake 13 to 17 minutes or until golden brown on top. Remove from oven to cooling rack; cool completely, about 30 minutes.
When rolls are cool, cut each into 9 pieces, cutting lengthwise into 3 pieces then cutting each piece into thirds. Remove half of pieces from baking dish. Distribute remaining half of pieces evenly in bottom of baking dish.
Cut block of cream cheese into 8 rows by 5 rows to make 40 small squares. Evenly distribute cream cheese squares over roll pieces in baking dish. Layer second half of roll pieces evenly over cream cheese. Set aside.
In large bowl, beat eggs, sugar, cinnamon, half-and-half and vanilla with whisk until well combined. Pour egg mixture evenly over top of casserole. With back of spoon, press mixture down so rolls pieces absorb as much of egg mixture as possible. Cover dish with foil; refrigerate overnight, 6 to 8 hours.
Heat oven to 350°F. Uncover baking dish; bake 35 to 45 minutes or until browned and set.
Place small scoops of icing over warm casserole; let stand until melted. With knife or metal spatula, carefully spread icing over top of casserole. Serve warm.