Put the butter, sugar, flour and egg in the food processor fitted with the steel dough blade. Turn on the food processor and process until everything is evenly combined (about 1 minute).
Cut the plums into slices and discard the pits.
Spray the non-stick 9-inch round baking dish with a non-stick cooking spray.
Take 2/3 of the dough mixture and put it in a baking dish. Press the dough with your fingers to form the bottom crust - the dough should line the bottom of the baking dish without any gaps.
Put the plum slices on top of the dough. Crumble the remaining 1/3 of the dough and put those dough crumbles on top of the plums.
Put the baking dish in the oven and bake the plum pie for 45 minutes.
Remove the plum pie from the oven. It will be very hot! Let cool for 15 minutes.