How to Make It
Preheat the oven to 350°. Butter a 10 1/2-inch springform pan. Line the bottom of the pan with parchment paper and butter the paper. In a medium skillet, toast the fennel seeds until fragrant, about 3 minutes. Transfer to a plate to cool. Melt the butter in the skillet. Add the fennel and cook over moderate heat until tender and golden brown, about 10 minutes. Let cool.
In a food processor, pulse the almonds until finely ground. Transfer to a small bowl. Repeat with the pistachios, adding them to the almonds. In a large bowl, using a handheld mixer, beat the egg yolks with the sugar at high speed until light in color, about 2 minutes. At low speed, blend in the toasted fennel seeds and the ground nuts. Stir in the cooked fennel.
In a large, stainless steel bowl, beat the egg whites to firm peaks. Fold one-third of the beaten whites into the cake batter to lighten it, then fold in the remaining whites until no streaks of whites remain. Scrape the batter into the prepared pan, and bake for about 40 minutes, or until the cake is just set. Transfer the cake to a rack and let cool for 20 minutes.
In a small skillet, toast the star anise, fennel and anise seeds over moderate heat until fragrant, about 3 minutes. Add the water and sugar and bring to a boil. Add the sliced fennel, cover and simmer over low heat until translucent, about 20 minutes. Let cool until warm.
Remove the sides of the springform pan. Transfer the cake to a platter and cut it into wedges. Place a slice of cake on each plate, drizzle some syrup on the side and dollop whipped cream on top.