In a medium saucepan, OFF HEAT, whisk together sugar, cornstarch, and salt. If making chocolate pudding, add cocoa powder. Very gradually (a few tbsp. at a time) whisk in coconut milk, taking care to dissolve cornstarch. Whisk in egg yolks.

Place saucepan on burner. Whisking constantly, cook over medium heat until the first large bubble forms and sputters. Reduce heat to low; still whisking, cook 1 minute. Remove from heat. Stir coconut oil and vanilla into hot pudding.

Either in individual bowls, or whole pan, place plastic wrap directly on surface of pudding. This is done to prevent skin from forming on pudding. Chill at least 3 hours and up to 3 days. Before serving, whisk pudding until smooth.