In a large cast iron skillet over mediumhigh heat, melt 3 tablespoons butter. When foaming subsides, add diced pumpkin. Brown for 5 minutes, stirring infrequently to caramelize. Add cardamom, black pepper, and allspice. Reduce heat to medium and add apples, along with 3 more tablespoons butter. Saute for 7 minutes, stirring occasionally. Turn heat to low and add maple sugar. Stir to combine, cover, and cook 25-30 minutes until the mixture is soft but still holds their shapes. Remove from heat and allow to cool.

On lightly floured parchment, roll one sheet of pastry into a square. Transfer to a rimmed baking sheet and refrigerate. Working the same way for the second, roll it once in each direction and refrigerate.

Using an 11” pastry tart ring, drape the square piece of puff so that sits evenly and does not stretch at contact point with the ring. Fill pastry with cooled pumpkin-apple mixture. Dot with remaining tablespoon of butter. If pastry becomes flabby in the process, chill for 5-10 minutes. Drape second puff sheet squarely on top. Trim pastry edge to 1 ½ inches all-around, rolling scraps for another use. Paint pastry with egg wash, then twist edge over itself to seal, working along the circumference until complete. Refrigerate for at least one hour, up to overnight.

Preheat oven to 400°. Beat egg in a small bowl. Remove pie from refrigerator and carefully lift tart ring. Paint egg wash all over, then bake pie for 25-35 minutes until golden. Check halfway through for even browning, rotating pan if needed.

Lower heat to 375° and bake for 10 more minutes or until crust is deeply golden. Cool on a wire rack for at least 15 minutes. Serve with whipped cream, ice cream, or creme fraiche.