Preheat oven to 375°F. Roll out pie dough and fit into a 9-inch pie dish, crimping edges. Prick bottom with a fork. Line with parchment paper and fill with pie weights or beans.
Bake for 15 minutes, then remove weights and parchment and bake for another 8 to 10 minutes, until lightly golden. Set aside to cool completely.
In a medium saucepan, whisk together granulated sugar, cornstarch, and salt until fully combined with no lumps.
Slowly whisk water into the sugar mixture until smooth. Cook over medium heat, whisking constantly, until mixture thickens and bubbles, about 5 to 7 minutes. Cook 1 minute more, then remove from heat.
Place beaten egg yolks in a small bowl. Slowly ladle about half a cup of hot sugar mixture into yolks, whisking constantly to temper. Pour tempered yolk mixture back into saucepan, whisking to combine.
Return saucepan to medium heat and cook for 2 to 3 more minutes, whisking constantly, until filling is thick and glossy. Remove from heat and whisk in butter until melted. Whisk in lemon juice and lemon zest until smooth.
Pour warm lemon filling into cooled, baked pie crust, spreading into an even layer. Press plastic wrap directly onto the surface to prevent skin from forming. Refrigerate for at least 3 hours, or until fully set.
Just before serving, beat chilled heavy cream, powdered sugar, and vanilla extract together until soft peaks form. Spread or pipe whipped cream over chilled pie. Slice with a sharp knife, wiping blade between cuts.