Preheat your oven to 350°F (175°C).
In a mixing bowl, combine flour, sugar, and salt. Cut in the butter until the mixture resembles coarse crumbs.
Add the egg yolk and ice water, mixing until the dough comes together. Press into a tart pan.
Bake the crust for 15 minutes, then let it cool.
For the filling, whisk together sugar, eggs, lemon juice, and lemon zest until smooth.
Stir in the heavy cream and chopped basil.
Pour the filling into the cooled crust and bake for another 15 minutes, or until set.
Let the tart cool before serving.