Preheat the oven to 325 degrees F. Grease two 4 ½ inch springform pans with shortening and dust with flour.
Sift the flour, salt, and baking powder together and set aside (or just mix them together well).
With a handheld electric mixer, beat the butter until creamy. Add the sugar and beat until light and fluffy. Using low speed, add the egg, then increase mixer speed and beat for about a minute, scraping sides of bowl; beat in the vanilla.
Fold the dry ingredients into the butter mixture with a heavy duty scraper. A soft dough should form. Scrape the dough into a pastry bag. Pipe a circle of dough over the bottom of each pan, then pipe an outer circle on top of that circle to contain the cream.
Put a large scoop of pastry cream in the center, making sure it doesn't touch the walls of the pan. Try to scoop it higher than the outer circle.
Carefully pipe remaining batter over the mount of pastry cream. Don't build up the sides, just do the best you can to cover the pastry cream so that it mounds in the center.
Brush tops owith a mixture of beaten egg and milk. Set on a rimmed baking sheet and bake for about 45 minutes at 325 until tops are golden brown and cakes appear set. Let cool for about 25 minutes in the pan, then carefully remove the rings and let cool completely.
At this point, you can chill the cakes or serve them at room temperature.