PREP: Cut 14 tbsp butter (straight from fridge) into small cubes. Place in the fridge until ready to use. Place the tart pan on a large tray. Grease the pan with nonstick cooking spray. Set aside.
CRUST: In a large food processor (or powerful blender), add cubed butter, 3/4 cup powdered sugar, and 2-1/2 cups flour. Pulse in 1-second pulses until the butter is in small pieces, about 20-25 pulses.
CRUST CONT.: Add in 1 egg yolk only (no whites!), 1 tsp. vanilla extract, 3/4 tsp. salt, and 2 tablespoons very cold water. Pulse until the dough begins to clump together, about 20-25 more 1-second pulses. The dough should be gathering together in large clumps, but still look a bit crumbly/shaggy. Dump the mixture from the food processor onto a clean work surface and roll/shape into a ball. Add a touch of flour only if needed (dough is too sticky). Add dough to prepared tart pan and press evenly into pan (don't stretch/pull, but rather gently coax and press) to cover the side and center as evenly as possible. Poke the bottom of the crust 8 times with a fork. (Don't press fork all the way through the crust-- only about 1/2 way.) Place in the freezer and chill for 20 minutes or cover and chill in the fridge overnight.
OVEN: Preheat the oven to 350 degrees F.
BAKE CRUST: Remove the tart from the freezer and place a sheet of parchment paper over the tart. Fill the tart with dried beans, rice, or pie weights (this is to weigh down the crust, ensuring it keeps shape). Bake for 25 minutes. Remove the foil and bake for another 5-10 minutes or until the edges are light brown and the bottom is nicely set. Remove and let cool until filling while making the filling.
FILLING: Meanwhile, add 4 eggs to a large bowl and set aside. In the food processor or blender used before, add 3/4 cup white sugar and the zest of 3 large lemons (about 2 tbsp packed zest). Pulse the two together until the zest is broken down, but we don't want to make the sugar into powdered sugar! Add this sugar mixture to the eggs along with 1/2 cup lemon juice, 1/2 cup cream, and a tiny pinch of salt. Thoroughly whisk until combined.
BAKE ENTIRE TART: Pour half of the lemon filling through a mesh strainer into the partially baked crust. Very carefully (so the lemon filling doesn't spill over the sides of the crust) transfer tray back to the oven and then pour the rest of the lemon filling in (this helps prevent spills and makes it easier to get in oven). Bake tart for 18-25 minutes or until tart is set with a very slight jiggle/wobble in center. Remove and let cool to room temperature before transferring to the fridge and chilling for at least 1 hour.
ENJOY: Remove the tart and slice. Use a hot, sharp knife (run it under hot water, dry with a towel) to make cuts into the tart. If desired, top with fresh berries and a sprinkle of powdered sugar (only top with berries right before eating!)