In a medium bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and salt until blended. Set aside.

In the bowl of an electric mixer fitted with a paddle attachment, beat together the butter and sugars at medium low speed until smooth. Add the egg and vanilla and mix until incorporated. Scrape down the sides of the bowl with a spatula, then begin to gradually add the flour mixture to the dough, mixing at low speed until just incorporated.

Place a sheet of parchment paper or plastic wrap on a large flat work surface. Divide the dough in half and roughly shape each half into a sphere with your hands. Place one half in the center of the plastic wrap and pat it down a bit, then lay another sheet of plastic wrap down on top of it. Roll it flat with a rolling pin into the shape of a circle until it is about 1/4 inch thick and 8 inches in diameter. Repeat with the other half of the dough.

Place the wrapped discs of dough on a baking sheet or cutting board and refrigerate for 2 hours.

Preheat the oven to 350 degrees Fahrenheit. Generously grease an 8-inch cake pan and set aside. Remove both discs of dough from the refrigerator and peel the wrapping off one of the discs. Place it in the bottom of the cake pan, pressing it into the bottom and up against the sides with your fingers so that it covers the entire bottom of the pan. Empty the jam or pastry cream onto the center of the dough and spread it slightly flat, making sure to leave a 2-inch border around the edge without filling so you can eventually seal the edges of the dough together.

Dip your finger in warm water and trace it around the edge of the dough in the pan. Peel the wrapping off the second disc of dough and gently place on top of the filling. Press the edges together, going around the edge of the circle, to seal in the filling.

Brush the top of the tart with the egg wash and drag a fork across the top to make a design. Place in the oven and bake for 40 to 45 minutes or until the top of the cake is golden brown. Remove from the oven and allow to cool for 5 to 10 minutes before gently running a knife around the edge of the pan and inverting the tart onto a wire rack. Immediately flip the tart back over so that it cools with the design facing up. Allow to cool for 20 minutes or so before serving.