In a mixing bowl, combine flour and powdered sugar. Cut in the cold butter until the mixture resembles coarse crumbs. Add the egg yolk and mix until the dough comes together.
Press the dough into a tart pan. Bake for 15 minutes or until lightly golden. Let it cool.
In another bowl, whisk together sugar, eggs, lemon juice, and lemon zest. Stir in the heavy cream and chopped basil.
Pour the filling into the cooled crust. Bake for 15 minutes or until the filling is set. Let it cool before serving.