Mix sugar, cocoa powder, cornstarch, and salt together in a saucepan; whisk in 1/4 cup almond milk until foamy and smooth. Continue adding almond milk, 1/4 cup at a time, to cocoa mixture until mixture is smooth and foamy each time. Place saucepan over medium-high heat and cook, stirring constantly, until mixture comes to a simmer and starts to thicken, about 5 minutes.
Remove saucepan from heat and stir in butter until melted and smooth. Add vanilla extract and mix well. Pour pudding into serving bowl and refrigerate until chilled, at least 30 minutes.