Preheat the oven to 375 degrees and spray your 9-inch pie pan with non-stick spray.
Slice your plums into ¼-inch slices and toss them into a large bowl (peeling is optional). Add the brown sugar, flour, lemon juice, cinnamon, and vanilla extract into the bowl with the plums. Mix all of the ingredients together thoroughly until the plums are well coated.
On a lightly floured surface, roll out one of the pie doughs using a rolling pin, turning the dough slightly each time until a circle forms. We want about an 11 to 12-inch circle diameter (if it's not a perfect circle, that's okay!). Place the dough into your 9-inch pie pan, carefully letting the excess pie dough hang over the sides. Pour the plum filling into the crust, including the juices. Cut off the excess pie dough that is hanging over the sides using a pairing knife.
Lattice Pie Crust: Lightly flour your surface again and begin rolling out your other pie crust into another 11 to 12-inch circle. Take a pizza cutter and cut the dough into 12 1-inch strips. Take 6 of those strips and lay them evenly spaced out on top of the pie filling vertically (up and down).
Fold back every other strip (3 total) so they're almost falling off of the pie. Lay one of the 6 unused pie dough strips horizontally and pull back down the 3 vertical strips that were hanging off the side of the pie.
Fold back the other 3 vertical strips as you did in the last step, letting them hang over the pie, and lay one of the 5 unused pie dough strips horizontally. Pull back down the 3 vertical strips. You should start to see the beginning of your woven design!
Continue with folding back every other vertical strip and laying down one of the unused pie dough strips horizontally until your lattice pie crust is completed. Use your fingers to pinch the excess pie dough from the strips around the edge of your pie pan. `
In a small bowl mix up your egg and use a brush to do an egg wash over the top of your lattice crust. This will give the crust a nice golden brown color as it bakes.
Bake your pie at 375 degrees for 20 minutes, then turn the temperature down to 350 degrees and bake for an additional 40-45 minutes. Allow your pie to cool at room temperature for 3 hours before slicing. This allows the pie to thicken up as it cools.