Preheat oven to 325°F. Line a 9x9 square baking pan with foil or parchment paper. Grease it well, set aside.
Using a hand mixer or stand mixer fitted with the paddle attachment, beat butter and sugar for 1-2 minutes, until smooth and combined. Add flour and salt and beat until just combined (the mixture will be crumbly, but it should hold together if you squeeze it with your fingertips).
Dump the dough into the prepared pan and press it gently into an even layer. Be careful not to pack it in too tightly, or the crust will be hard to cut through. If necessary, moisten your fingers or palm with water to keep the dough from sticking. Bake the crust for 10 minutes. While the crust is baking, prepare the filling.
Filling
In the bowl of a stand mixer fitted with paddle attachment (or with a hand mixer), beat cream cheese until smooth and combined. Add sugar and flour and beat until well combined. Add eggs, lemon zest and vanilla and beat until combined. Slowly add the lemon juice (I like to do this with the mixer running), beating until the lemon juice is fully incorporated.
Pour the batter into the crust and return to the oven for about 25 minutes, or until the filling is set. Place the pan on a cooling rack, cool to room temp, then cover and refrigerate until completely chilled (several hours).
Notes
It is good to serve these slightly chilled. Remove them from the fridge 30 minutes before serving to allow the crust to soften up a bit. Serve topped with whipped cream.