CASSEROLE: Spray a 9x13 baking dish with cooking spray. Spread the bread cubes in the dish in an even layer. In a 4 cup measuring cup or medium bowl, whisk (or use an immersion blender) and mix together the eggs, milk, sour cream, vanilla, and ¼ cup (use ½ cup if you used brioche or challah) sugar until combined. It's okay if you see little specks of the sour cream (if you whisked.) Pour the liquid evenly over the bread pieces. Cover the baking dish with plastic wrap and refrigerate overnight, or at least 6-8 hours.
CINNAMON SUGAR: Position a rack in the center of the oven and preheat the oven to 350ºF. Melt the butter in a microwave-safe bowl. Whisk in ½ cup sugar, cinnamon, and nutmeg, until combined. Drizzle this prepared mixture over the casserole.
BAKE: Bake the casserole uncovered for 28-35 minutes or until the casserole is browning and set in the center (test with a toothpick.) If at any point it starts browning too much, cover loosely with foil. Allow the casserole to cool for 10-15 minutes before icing.
ICING: While the casserole is baking, beat the softened butter and cream cheese together using a hand mixer, until smooth. Pour in the vanilla, lemon juice, and powdered sugar, and mix until smooth. Once the icing is combined, add a teaspoon of milk at a time, mixing thoroughly before adding the next teaspoon. I didn’t need more than 2 teaspoons, the more you mix, the more the icing will thin naturally. But add milk until the icing reaches your desired consistency. I like the consistency to be a little thick so that it doesn’t become too loose when you drizzle over the warm casserole. Tilt the bowl and drizzle the prepared icing over the warm cinnamon roll casserole or pour the icing into a piping bag, snip off the end, and drizzle in a pretty design! Serve warm!