Preheat the oven to 400 degrees Fahrenheit/205 degrees Celsius.
Roll out the puff pastry sheets -- one 11 inches square and the other 10 inches. Flour the surface lightly if you need to in order to prevent the puff pastry from sticking as you roll.
Cut out discs in the puff pastry sheets using a 9-inch pie plate as a template. The first disc, which will be the bottom crust, should be about an inch wider than the pie plate. The second disc, the top crust, should be the same diameter as the pie plate.
Fit the larger puff pastry disc inside the pie plate and over the edges.
Scoop out the frangipane filling into pie plate. Use a knife or offset spatula to spread it evenly across the bottom of the crust.
Pour the cooled strawberry rhubarb filling over the frangipane and smooth into an even layer.
Fit the remaining puff pastry disc over the top of the pie plate and crimp the edges of the top and bottom crust together to create a tight seal.
Use a sharp knife to make a hole in the top of the crust to let the steam escape. Then, moving from the top of the crust to the bottom, score the crust in curved lines. The cuts should be superficial--don't cut through the pastry.
Mix a teaspoon of oil and a teaspoon of nondairy milk in a small bowl. Brush it on top of the crust. This is optional--it helps give the crust a nice color.
Place the pithivier pie plate on a baking sheet in the preheated oven. Bake 40-45 minutes until the puff pastry is golden and the juices are bubbling. Optionally, about five minutes before baking ends, remove pithivier from the oven and dust some powdered sugar on top. Return to the oven for five minutes.
Cool the pithivier at room temperature for 4-5 hours until completely cool. Slice and eat.