Combine the sugar and the flour in a heavy-based saucepan. Whisk just to mix. Add the orange juice and egg yolks and whisk vigorously again to combine. Put the saucepan over medium-high heat and cook, whisking constantly, until the mixture boils (3 to 4 minutes). Cook another 1 minute, stirring constantly (the mixture will thicken noticeably and become less cloudy). Be sure it boils for 1 minute so that the filling will thicken enough to support the cake. Remove from the heat and stir in the butter. Transfer to a bowl, cover with plastic wrap (lay the wrap directly on the filling's surface), and refrigerate. Chill thoroughly before using.

Heat the oven to 350 degrees F. Sift together the flour, baking powder, and salt. Grease two 9x1-1/2-inch cake pans and line the bottom of each with a round of kitchen parchment. Lightly flour the sides and bottom of each pan.

In a mixer, cream together the butter, shortening, and zest. Gradually add the sugar, creaming until the mixture is light and fluffy. Scrape down the sides of the bowl. Add the eggs, one at a time, mixing well between additions and scraping down the sides.

Add the sifted dry ingredients alternately with the orange juice to the creamed mixture, beating well on low speed after each addition. Pour equal amounts of the batter into the two prepared cake pans. Tap the pans on the counter before putting them in the oven to remove any air bubbles and to even the batter. Bake until a toothpick inserted in the middle comes out clean, about 28 minutes. Cool the cake layers in the pans for 10 minutes and then loosen the layers by running a knife between the cake and the edge of the pan. Remove the layers from the pans and put them on a rack to continue cooling.

Cream the butter in the mixer. Add the confectioners' sugar and salt and combine thoroughly. Add the orange zest and mix to combine. Add the orange juice and mix on high speed until well blended, scraping down the sides. It will be light and creamy. Refrigerate if not using right away.

When all the components are cool, put one cake layer on a cake stand or a cardboard cake round. Spread the orange filling over the cake to make a 1/4-inch layer. You'll have about 1/3 cup extra filling; serve it alongside the cake, if you like. Put the second layer on top of the first and refrigerate the cake until the filling has chilled again and firmed up, about 45 minutes.

Loosen the frosting by beating with a spatula (if it's very stiff, beat it with an electric mixer). Using an icing spatula, spread just a very thin layer of frosting over the whole cake (this is called a "crumb coat" because it secures loose crumbs) and refrigerate the cake to let the frosting firm up, about 10 minutes. Put on the final coat of frosting, taking care to work gently, as the top layer of the cake tends to slide around ever so slightly because of the filling. If it slides, just push it back. Create a pattern on the frosting using the icing spatula (heat it up under warm water and dry it). Transfer the cake (on its cardboard or by lifting it with spatulas) to a cake plate or pedestal.

Twist the orange slices into "S" shapes and put seven or eight around the top of the cake. Tuck a pair of mint leaves into each orange twist.