Heat oven to 350°F. Lightly grease 9-inch glass pie plate with shortening, or spray with CRISCO® Original No-Stick Cooking Spray. Separate dough into 5 rolls; set icing aside. Unroll 1 roll into long strip of dough; reroll loosely and place in center of pie plate. Unroll second roll; loosely wrap around first roll, cinnamon side in. Replace any cinnamon that falls off. Repeat with remaining rolls, coiling dough in pie plate into spiral shape.
In small bowl, beat remaining ingredients except icing with electric mixer on medium speed until smooth. Spoon cream cheese mixture into decorating bag with tip or gallon-size resealable food-storage plastic bag with 1/2-inch hole cut in bottom corner. With tip or corner of bag about halfway down into rolls, pipe mixture between strips of dough, starting at center and working to edge of pan, using all of mixture.
Bake 25 to 35 minutes or until center is thoroughly baked and edges are deep golden brown. Cool 5 minutes. Meanwhile, remove cover from icing; microwave on Medium (50%) 10 to 15 seconds or until thin enough to drizzle.
Drizzle icing over warm coffee cake. Cut into wedges. Serve warm.