In a saucepan, whisk sugar and cornstarch together.
In a bowl, whisk egg yolks and milk until smooth.
Gradually add the milk mixture into the dry ingredients, whisking well.
Cook over medium-low heat, whisking constantly until thickened and gently boiling (6–8 minutes).
Remove from heat, then stir in butter and vanilla until smooth.
Transfer custard to a bowl, cover with plastic wrap touching the surface, and let cool completely.
Fold in whipped topping (if using) and refrigerate.
Dip biscuits briefly in milk (1 second per side).
Arrange a layer in a 9x9-inch dish.
Spread half of the custard over the biscuits.
Add another biscuit layer, then remaining custard.
Finish with a final biscuit layer.
Refrigerate for at least 4 hours to set.
Melt chocolate with milk using microwave or bain-marie.
Pour over the cake and spread evenly.
Chill for another 20–30 minutes until set.
Slice and serve your Vanilla No Bake Biscuit Cake.