In a medium saucepan, combine 1 cup of sugar, 1/3 cup of unsweetened cocoa powder, 1/4 cup of cornstarch, and a pinch of salt. Whisk until well blended.

Slowly pour in 2 3/4 cups of whole milk while whisking constantly. Place the saucepan over medium heat until it starts to warm and steam, about 5 minutes.

Stir continuously until the mixture reaches a full boil and thickens significantly, about 8-10 minutes.

Remove from heat and stir in 2 tablespoons of unsalted butter and 1 teaspoon of pure vanilla extract until fully combined.

Pour the chocolate pudding into individual bowls, letting it cool at room temperature for about 15 minutes.

Cover with plastic wrap and refrigerate for at least 2 hours to firm up.

Serve as desired, garnished with whipped cream or fresh berries.