Whisk sugar, cocoa powder, cornstarch, and salt together in a saucepan off the stove. Add 1/4 cup almond milk; whisk until smooth and foamy. Continue adding almond milk, 1/4 cup at a time, whisking after each addition.

Place the saucepan over medium-high heat and cook, stirring constantly, until mixture comes to a simmer and starts to thicken, about 5 minutes.

Remove from the heat and stir in butter until melted and smooth. Stir in vanilla, then pour pudding into a serving bowl. Cover and refrigerate until chilled, at least 30 minutes.