In a medium saucepan, combine ½ cup granulated sugar, ¼ cup unsweetened cocoa powder, ¼ cup cornstarch, and a pinch of salt. Whisk these dry ingredients together thoroughly until well combined.

Gradually pour in 2 ¾ cups of milk while vigorously whisking the mixture until smooth.

Place the saucepan over medium heat and cook, stirring constantly until the mixture begins to bubble and thickens, around 5–7 minutes.

Once it reaches a gentle boil, continue stirring consistently for an additional minute to develop the rich chocolate flavor.

Remove from heat and stir in 2 tablespoons of butter and 1 teaspoon of vanilla extract until smooth and velvety.

Transfer into bowls or dessert cups. Cover with plastic wrap to prevent skin formation while cooling. Serve warm or chill for 30 minutes.