In a medium saucepan (no heat), add sugar, cocoa, cornstarch, and salt and mix together well.

Add ¼ cup oat milk to sugar mixture, whisking together. Continue to add in small amounts, whisking after each addition till smooth.

Turn on heat to medium and bring to a simmer, whisking continuously. Once simmering with bubbles around the edges, reduce heat to low. Continue to cook, stirring frequently, till thickened, about 2 minutes.

Remove from heat and add chocolate chips and vanilla. Stir till melted and incorporated throughout.

Transfer to an airtight container. Place saran wrap directly onto the surface of the pudding and place airtight cover on top.

Place in refrigerator at least 2 hours or overnight.