Prepare an 8-inch pie pan with the pie crust (homemade or store-bought) and set it aside.
Preheat the oven to 180°C (350°F).
In a large mixing bowl, beat the softened vegan cream cheese and sugar on low speed until smooth and creamy.
With the mixer still on low, add the cornstarch, milk of choice, lemon juice, and vanilla extract, and mix until combined.
Increase the mixer to high and beat until the filling is completely smooth and airy.
Pour or spoon the cheesecake filling into the prepared pie crust and smooth the top with a spatula.
Bake in the preheated oven for 40–45 minutes, until the edges are set and the center is slightly jiggly.
Remove the cheesecake from the oven and let it cool completely on a wire rack, then refrigerate for at least 4 hours or overnight before serving.