Brush crust with egg yolk and bake according to the crust's directions.
Cool slightly.
Spread softened butter over the crust and refrigerate while you make the filling.
Filling
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.
Glaze
To make the glaze, stir the vinegar and powdered sugar together. Brush or pour as much or as little glaze as desired over top.
Refrigerate until serving, up to 6 hours.
Notes
Adding the hot milk to the pale yellow mixture before putting the whole mixture back into the pot is done to prevent the eggs from heating up too fast. In baking, you need to heat eggs gradually or they could turn into scrambled eggs, and you don't want a scrambled egg filling in this tart - you want a custard filling!When making the balsamic glaze, you can create whatever consistency you would like. Add more balsamic for a thinner consistency, and more powdered sugar if you are going for a thicker glaze.