Preheat and Prep: Preheat oven to 325°F (160°C) and butter an 8-inch round cake pan or medium heatproof skillet. Place the pan or skillet inside a larger pan, such as a 13 ½-by-10-inch roasting pan. This creates the water bath.

Melt Butter and Sugar: In a medium saucepan over medium-low heat, cook the butter and granulated sugar, stirring frequently, until the butter melts and the sugar dissolves, 7 to 9 minutes.

Add Chocolate: Remove the saucepan from the heat and stir in the chopped bittersweet chocolate. Let it cool for 5 minutes.

Whisk in Eggs and Baileys: Whisk in the eggs and 2 tablespoons of the Baileys Irish Cream.

Combine Dry Ingredients: In a medium bowl, whisk together the cocoa powder, flour, and salt.

Combine Wet and Dry: Fold the dry ingredients into the butter mixture, then stir until the mixture resembles wet brownie batter.

Pour Batter: Pour the batter into the prepared pan (the smaller pan inside the larger pan).

Add Water: Pour hot water into the larger pan until it reaches halfway up the sides of the smaller pan. This creates the water bath, which ensures even cooking and a moist, pudding-like texture.

Bake: Bake the brownie pudding until a flaky crust forms, resembling the top of a traditional brownie, and the center is slightly underdone and almost jiggly, 30 to 40 minutes.

Cool: Let the brownie pudding cool slightly.

Make Whipped Cream: Meanwhile, make the Baileys whipped cream. In a medium bowl, using an electric mixer on medium-high speed, beat the heavy cream and the remaining 1 tablespoon of Baileys Irish Cream until medium peaks form.

Serve: Top the brownie pudding with the whipped cream and serve