Preheat the oven to 350°F (175°C). Butter three 8-inch round cake pans. Line the bottom of each pan with a round of parchment or waxed paper cut to to fit and butter the paper.
Spread the pistachios on a rimmed baking sheet and slide it in the oven for 7 to 10 minutes, or until lightly colored. Transfer the pistachios to a plate and let cool completely. Finely chop the pistachios. Set 1/4 cup aside for sprinkling.
Dump the remaining 1/2 cup pistachios in a food processor. Add the sugar and pulse just enough to grind them finely. Pour the nuts and sugar into the bowl of a stand mixer, add the flour, baking powder, and salt, and blend on low for 30 seconds. Add the butter, milk, and vanilla and, with the mixer still on low, beat until completely incorporated.
Increase the speed to medium and beat until light and fluffy, 2 to 3 minutes. Add the beaten eggs in 2 or 3 additions, scraping down the sides of the bowl well and mixing only long enough to blend after each addition. Divide the batter evenly among the 3 prepared pans, smoothing the surface with a spatula.
Bake for about 25 minutes, or until a cake tester or wooden toothpick inserted in the center comes out clean. Let the cakes cool in the pans for 10 minutes. Turn the cakes out onto wire racks, carefully peel off the paper liners, and let them cool completely.
Make the marzipan
Crumble the almond paste into the bowl of a stand mixer. Turn the mixer on low speed to soften the almond paste. Add the confectioners’ sugar and corn syrup and beat until smooth. Wrap well in plastic so it doesn’t dry out and let rest at room temperature for 1 to 2 hours before rolling out.
Make the dark ganache glaze
Chop the chocolate coarsely and put it in a heatproof bowl. In a small saucepan, bring the cream to a bare simmer. Pour the hot cream over the chocolate and let it stand for 5 minutes. Whisk until smooth and use the glaze soon after making so that it doesn’t set.
Assemble the cake
Roll out 1/3 of the marzipan on a work surface lightly dusted with confectioners’ sugar to about 1/8 inch thickness.
Place an empty cake pan upside down on the marzipan and trim around it with a small knife to make an 8-inch round. Repeat 2 more times with the remaining marzipan. Save all your scraps to make marzipan roses for decoration, if you like. (See instructions below the recipe.)
Place a cake layer on a cake board or cake stand, flat side up. Spread 1/4 cup preserves evenly over the top, leaving a 1/4-inch plain border all around. Place 1 marzipan round on top of the preserves and spread 1/3 cup dark ganache glaze over the marzipan so that it completely covers the surface. Repeat with the second cake layer, adding more preserves, another round of marzipan, and more dark chocolate ganache glaze. Top with the third cake layer. Spread the last of the apricot preserves over the top of the cake and cover it with the last round of marzipan.
Place the cake on a wire cooling rack nestled in a baking pan. Pour the remaining ganache glaze over the cake, in several additions, spreading to coat the top and sides. Allow the ganache to set. Garnish the cake with the reserved chopped toasted pistachio nuts and a single marzipan rose or several smaller roses.
First, tint the marzipan, if desired, by kneading in a tiny amount paste food coloring, dabbing just a small bit of paste onto the marzipan with the tip of a toothpick. Flatten the tinted marzipan into a disk and roll out on a work surface dusted with confectioners’ sugar or between 2 sheets waxed paper to a sheet 1/8 inch thick.
With a 1 1/2-inch round cookie cutter, cut out 8 or 9 circles. Cover all the marzipan you are not using immediately with plastic wrap so it doesn’t dry out.
Roll a piece of marzipan into a ball the size of a marble and pinch with your fingers to shape into a cone about 1 to 1 1/4 inches high, tapering to a fine point at the top.
Take another round of marzipan and wrap it like a petal around the cone, pinching it at the bottom to adhere and at the top to thin and ruffle slightly like a flower. Repeat with the remaining “petals,” overlapping slightly as you work your way around. If necessary, use a little water to help glue the marzipan in place.