Mix sugar, flour, corn starch, and egg yolks till thick and pale yellow.
Combine milk and basil in a saucepan and bring to a boil. Immediately remove from heat.
Strain out the basil, pour about ⅓ of the milk into the pale yellow mixture, then pour the mixture back into the sauce pan.
Heat over medium, whisking constantly until thickened. When mixture begins to boil, cook for one more minute then remove from heat.
Let cool, then spread cooled filling into cooled tart shell.
Lay the sliced strawberries over the top of the cream in a single layer.