Place the eggs and yolks in the carafe of a blender and combine on lowest speed for 30 seconds. Slowly add the sugar, over 30 seconds, add the hot chocolate mix, and blend until incorporated, about 30 seconds. Add the half and half, milk, espresso and vanilla and blend until well combined, about 30 seconds.
Butter a 9-by-13-inch metal pan with 1 tablespoon of the butter and place the cubed bread in the pan. Spread the chocolate on top of the bread and slowly pour in the custard. Press down on mixture with a spatula or back of a spoon to thoroughly saturate. Cover and set aside at room temperature for 2 hours or refrigerate for up to 8 hours.
Heat oven to 325°F.
Bake uncovered until the internal temperature reaches at least 170°F, approximately 45 minutes. Set the oven to the high broil setting with the oven door ajar. Remove the bread pudding from the oven.
Pour the melted butter into a spray bottle and spritz the top of the bread pudding. Return to the middle rack and broil for 4 to 5 minutes. Remove to a cooling rack for 15 minutes before serving.