Step 1: Prep the Oven and Ingredients
First, preheat your oven to 325°F. Lightly grease the inside of a 9-inch skillet with butter. Next, melt the 1 cup of unsalted butter and set it aside to cool completely. In a separate bowl, sift the 3/4 cup of dutch cocoa powder and 1/2 cup of all-purpose flour together, then set the mixture aside.

Step 2: Whip the Egg Base
In your mixer, combine the 4 large eggs and 2 cups of white sugar. Beat this mixture on medium-high speed for a full 5 to 10 minutes until it becomes very thick, voluminous, and a pale light yellow.

Step 3: Combine Wet and Dry
After the 10 minutes of whipping, reduce the mixer speed to low. Add the 3 teaspoons of vanilla extract, the 2 teaspoons of optional coffee extract, and the sifted cocoa powder and flour mixture. Mix very slowly, only until everything is just combined.

Step 4: Add Cooled Butter
Slowly pour in the cooled melted butter. Mix again on low speed just until the butter is fully incorporated and the batter is homogeneous. Pro Tip: Do not overmix the batter at this stage! Mix only until the butter disappears into the batter to preserve the rich, fudgy, pudding-like texture.

Step 5: Bake in a Water Bath
Pour the finished mixture into the prepared 9-inch skillet. Place the skillet into a larger baking pan. Add warm water to the larger pan until the water level comes halfway up the side of the skillet. Carefully place the entire setup into the preheated oven and bake for 60 minutes.

Step 6: Cool and Serve
The pudding will look under-baked and very soft when it comes out this is normal! Remove the skillet from the water and place it directly into the fridge to cool completely. Serve the chilled or slightly cooled pudding in the skillet, best enjoyed with a scoop of vanilla ice cream on the side.