Warm the unsweetened oat milk in a small saucepan over medium heat until it's hot but not boiling.
In a separate bowl, sift the cocoa powder to remove any lumps. Add the sifted cocoa powder to the saucepan, stirring constantly to combine with the milk.
Add the finely chopped chocolate or chocolate chips to the saucepan. Continue stirring until the chocolate is completely melted and the mixture is smooth.
Stir in the granulated sugar, adjusting the sweetness according to your preferences.
Add the vanilla extract and continue heating the hot chocolate until it reaches your desired temperature. Be careful not to let it boil.
Once heated, pour the hot chocolate into mugs.
Optional: Top with whipped cream, chocolate shavings, dark chocolate chips, or mini marshmallows for an extra indulgent touch.
Serve immediately, and enjoy your rich and creamy Homemade Hot Chocolate with Oat Milk.