2 large whole eggs
3 egg yolks
3/4 cup sugar
1/2 cup hot chocolate mix
3 cups half-and-half
1 cup whole milk
2 ounces espresso, slightly cooled
1 tablespoon vanilla extract
2 tablespoons unsalted butter, melted and divided
18 ounces stale challah bread, cut into 1-inch cubes
6 ounces bittersweet chocolate, broken into 1/2-inch pieces