Cut the cold unsalted butter into small cubes and refrigerate. Grease the tart pan with cooking spray and place it on a large tray. Set aside.
In a large food processor or powerful blender, add cubed butter, powdered sugar, and flour. Pulse in 1-second intervals until the butter forms small pieces, about 20–25 pulses.
Add egg yolk, vanilla extract, salt, and the very cold water. Pulse until the dough starts to clump, about 20–25 more pulses. The dough should form large clumps but still appear a bit crumbly.
Transfer the mixture to a clean work surface and shape it into a ball. Add a touch of flour if needed (if the dough is too sticky). Press the dough evenly into the prepared tart pan, covering the sides and center. Poke the bottom of the crust 8 times with a fork, only halfway through. Freeze for 20 minutes or cover and chill in the fridge overnight.
Preheat oven to 350°F.
Remove tart from freezer. Place a sheet of parchment paper over it and fill with dried beans, rice, or pie weights to keep the crust in shape. Bake for 25 minutes. Remove the weights and parchment, then bake another 5–10 minutes until the edges are light brown and the bottom is set. Let cool while preparing the filling.
Meanwhile, add eggs to a large bowl. In the same food processor or blender, add granulated sugar and the zest of 3 large lemons (about 2 tablespoons packed). Pulse until the zest is broken down, but avoid turning the sugar into powdered sugar. Add this sugar mixture to the eggs along with 1/2 cup lemon juice, cream, and a pinch of salt. Whisk thoroughly until combined.
Pour half the lemon filling through a mesh strainer into partially baked crust. Carefully transfer tray back to oven, then pour in remaining filling. Bake for 18–25 minutes, or until tart is set with a slight jiggle in the center. Let cool to room temperature, then refrigerate for at least 1 hour.
Remove the tart and slice it using a hot, sharp knife (run under hot water and dry with a towel). If desired, top with fresh berries and a sprinkle of powdered sugar just before serving.
