Preheat the oven to 350 degrees. Toast the almonds on a baking sheet until lightly golden, 6 to 7 minutes. Cool slightly, then pulse in a food processor until finely ground, but not pasty.
Melt 12 tablespoons butter and the chocolate in a heatproof bowl set over a saucepan of simmering water (do not let the bowl touch the water). Stir until the chocolate is smooth, then remove from the heat and cool slightly. Grease the bottom and sides of a 9-inch springform pan with butter and coat with the breadcrumbs, tapping out the excess.
Set aside 2 tablespoons granulated sugar. Combine the 6 egg yolks and the remaining sugar in a stand mixer and beat with the paddle attachment on medium-high until thick and pale, about 3 minutes. Add the orange zest, rum and salt, then beat in the melted chocolate until smooth. Mix in the ground almonds until just combined.
In a clean bowl, beat the 3 egg whites with a mixer until foamy. Gradually beat in the reserved 2 tablespoons granulated sugar on high speed until almost stiff. Stir one-third of the whites into the chocolate batter, then gently fold in the rest. Spread the batter in the prepared pan and bake until the top is firm and cracked (a toothpick inserted into the cake will be fudgy), 35 to 40 minutes. Cool on a rack 10 minutes, then run a knife around the edge of the pan and remove the ring. Serve warm or at room temperature. Garnish with confectioners' sugar and whipped cream, if desired.