FOR CRUST: Dice the butter and return it to the refrigerator while you prepare the flour mixture. Place measured coconut oil in the refrigerator as well.
Place the flour and sugar in the bowl of a food processor fitted with a steel blade and pulse a few times to mix. Add the butter and coconut oil. Pulse 10-12 times, until the butter is the size of peas.
With the machine running, pour the ice water down the feed tube and pulse the machine until the dough begins to form a ball.
Dump out on a floured board and roll into a ball. Wrap in plastic wrap and refrigerate for 30 minutes. Cut the dough in half. Roll each piece on a well-floured board into a circle, rolling from the center to the edge, turning and flouring the dough to make sure it doesn't stick to the board. Fold the dough in half, place in a pie pan, and unfold to fit the pan. Repeat with the top crust.
FOR FILLING: Slice plums, skin on, into ΒΌ inch slices and place in a medium saucepan. Using a vegetable peeler, peel half of the lemon into large strips avoiding too much white pith.
Measure 3 tablespoons of rum into a 1-cup measuring cup and full the rest with water. Add rum/water, sugar, vanilla bean powder, and lemon peel to the saucepan. Stir to combine. Sprinkle the cornstarch over the plum mixture and gently stir to combine.
Cook over medium-low heat until the sugar has dissolved and mixture has thickened, 8-10 minutes.
Remove the strips of lemon peel. Cool to room temperature before filling pie.
For a shine and light browning, brush crust with an egg white that was lightly beaten with 1 teaspoon of water. Bake at 375 degrees F for 35 minutes, or until golden brown. Enjoy!