Preheat oven to 350°F. Line a 17- x 12-inch rimmed baking sheet with parchment paper, and set aside. Stir together ground cinnamon and 1 ¼ cups of the granulated sugar in a shallow bowl. Place melted butter in a separate small, shallow bowl. Dip each roll in melted butter, turning to coat evenly; roll in cinnamon sugar to coat evenly. Place on prepared baking sheet (rolls will be almost touching). 

Bake in preheated oven just until puffed and cooked through, about 20 minutes. Let rolls stand until cool enough to handle, 20 to 30 minutes.

Lightly grease (with cooking spray) an 11-inch round or oval 2-quart baking dish. Whisk together eggs, half-and-half, salt, 2 teaspoons of the vanilla, and remaining ¼ cup sugar in a large bowl. Hold each baked roll over prepared dish, tear into bite-size pieces, and arrange in prepared dish. Pour egg mixture evenly over top. Cover with plastic wrap, gently pressing to submerge as many roll pieces in custard as possible. Chill at least 4 hours or up to 16 hours. 

Preheat oven to 350°F. Uncover the casserole, and let stand at room temperature while oven preheats. Bake until golden and set, 30 to 35 minutes. Set aside to cool slightly. 

While casserole bakes, combine cream cheese and whole milk in a small saucepan over medium. Cook, whisking constantly, until cream cheese melts and the mixture is smooth, about 2 minutes. Whisk in powdered sugar and remaining 1 teaspoon vanilla until smooth. Drizzle over warm casserole.