In a medium saucepan, combine 3/4 cup granulated sugar, 1/3 cup unsweetened cocoa powder, 1/4 cup cornstarch, a pinch of salt, and 2 tablespoons of instant coffee granules (if using). Stir thoroughly.

Slowly pour in 2 3/4 cups of milk while whisking continuously. Place the saucepan over medium heat, stirring often.

Once the mixture starts simmering, keep stirring constantly for 1 to 2 minutes until it thickens.

Remove from heat, stir in 2 tablespoons of butter and 1 teaspoon of vanilla extract until fully melted.

Transfer the pudding into a storage container, press plastic wrap directly against the surface to prevent a skin.

Place in the refrigerator to chill for about 2 hours.