In a bowl, whisk the oat milk and cornstarch until smooth and free of lumps.
Transfer the mixture to a medium saucepan and stir in the granulated sugar. Heat over medium heat, stirring constantly until the custard reaches a simmer and thickens, about 5-10 minutes.
Stir in the vanilla bean paste. Pour the custard into a bowl. Cover the surface with plastic wrap to prevent a skin from forming. Chill.