For the custard: Heat the milk and chopped basil leaves on medium-low until just before the milk boils. Strain the basil from the milk and discard the leaves.
 

In a medium bowl, whisk the egg yolks, sugar, vanilla, and flour or cornstarch until smooth and creamy. Very gently and slowly pour the hot milk onto the egg mixture, whisking continuously while pouring the milk. Mix well for a few moments and then pour the whole mixture back into the same saucepan. Return the saucepan to the stovetop and heat on medium-low heat until the liquid begins to boil.
 

Continue cooking for about 5 minutes until thickened, stirring constantly to avoid lumps. If your custard is lumpy, simply pass it through a mesh strainer. Remove from heat and cool. Refrigerate if not using right away.