For the Crust:
Prep the butter: Cut the cold butter into chunks and keep it in the freezer until you're ready to use it.
Combine dry ingredients: In a food processor, add the flour, sugar, salt, vanilla extract, and vanilla bean. Then, add the butter and pulse 10 times until the mixture resembles small crumbs or pea-sized bits.
Add water: Fill a glass with ice water and measure out 4-5oz (120-150ml). Slowly add the water to the food processor while pulsing. Stop as soon as the dough starts to clump and pull away from the sides. You want it just combined, not overly wet.
Chill the dough: Transfer the dough to the refrigerator while you prepare the filling. If the dough isn’t too wet, you can roll it out immediately, which is handy if you're in a rush.
For the Plum Filling:
Prep the fruit: Wash, pit, and quarter the plums. In a large bowl, toss the plums with the zest and juice of one lime.
Mix dry ingredients: In a separate bowl, combine the sugar, flour, and cornstarch. Sprinkle this mixture over the plums and toss until they are evenly coated. Be sure to scrape any remaining dry mixture into the bowl of plums.
Roll the dough: Grab the chilled dough and divide it in half. Roll out the bottom half and place it in your pie dish. A metal pie tin will yield the best crust, but ceramic works well if that's what you have on hand.
Assemble the pie: Fill the bottom crust with the prepared plum filling, then dot the top of the filling with small pieces of butter to enhance the richness as it bakes.
Top the pie: Roll out the remaining dough. Cut it into four wide strips to create a rough lattice on top of the pie, leaving space for steam to escape.
Finish the top: Brush the top crust with an egg wash and sprinkle with raw turbinado sugar. Create the egg wash by whisking together an egg and a teaspoon of water.
Bake: Bake the pie at 425°F (218°C) for 15 minutes. Then, reduce the heat to 350°F (180°C) and continue baking for an additional 30 minutes.