Chef Bobby's Boozy Stuffed French Toast

1 challah or brioche loaf (it is best if the bread is 1-3 days old and slightly stale) 1 (8-ounce) package cream cheese, softened ¼ cup granulated sugar 1 teaspoon ground cinnamon ¼ teaspoon fine sea salt 1 cup half-and-half 3 large eggs 1 teaspoon pure vanilla extract 6-8 tablespoons unsalted butter, divided Toppings Suggestions: Luxardo 🍒 whipped cream, powdered sugar, maple syrup, and/or fresh berries Place 8 ounces cream cheese in a medium bowl or bowl of a stand mixer and let sit at room temperature until softened, about 30 minutes. Add 1/4 cup powdered sugar, 1 teaspoon of the vanilla extract, and 1/4 teaspoon of the kosher salt. Beat with the paddle attachment on high speed until smooth and spreadable, about 45 seconds. Divide the cream cheese mixture onto 6 (1/2-inch-thick) slices of brioche or challah bread. Spread onto the bread, concentrating more towards the middle so that the filling doesn’t spill out. Top with the remaining 6 bread slices and gently press down on each sandwich. Place 3 large eggs, 1 cup milk, 1 teaspoon ground cinnamon, and the remaining 1 teaspoon vanilla extract and 1/4 teaspoon kosher salt in a wide, flat bowl or pie plate. Whisk to combine. Heat a 12-inch nonstick frying pan over medium-low heat (or an electric griddle set to 325ºF). Add 1 tablespoon of the unsalted butter and swirl to coat the pan (or brush over the griddle). Dip each sandwich in the egg mixture on both sides and place them on the skillet (do 2 at a time) or griddle. Cook until golden-brown, 3 to 4 minutes per side. Add 1 tablespoon unsalted butter to the skillet in between each batch. Dust with powdered sugar or drizzle with maple syrup and serve immediately.