Preheat the oven to 375°F. Butter and flour one 8-inch cake pan.
Combine the almonds and flour in a food processor and grind until fine. (The addition of flour prevents the almonds from forming a paste. Purchased almond meal may be substituted, but will result in a torte with a different texture.) Whisk in 1/3 cup granulated cane sugar.
In a small bowl combine the egg yolks and vanilla extract and whisk by hand. Set aside.
Put the butter in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until the butter is creamy. Slowly beat in the melted chocolate.
On medium speed, beat in the egg yolk mixture until fully incorporated, approximately 2 minutes.
Using a rubber spatula, fold in the almond mixture until just blended. Fold in the beets and set aside.
Place the eggs whites in a separate bowl on a stand mixer fitted with the whisk attachment.
Beat the eggs on medium speed. When the whites are opaque and start to increase in volume, add the remaining 1/3 cup granulated cane sugar. When they start to become stiff, increase the speed to high and beat until the whites start to lose their shine but still look wet. They will hang in medium-stiff peaks when the whip is lifted form the bowl.
Fold about one-third of the whites into the batter with a rubber spatula. Fold in the rest of the whites just until no white streaks remain.
Distribute the mixture evenly into the prepared cake pan.
Place in the oven on the middle shelf and reduce the oven temperature to 350°F.
Bake for 30 minutes. This is a dense, moist cake and will rise very little. A skewer inserted into the center will have a moist crumb; it will not come out clean.
Let cool completely in the pan on a wire rack. When cool, remove the torte and coat with your favorite chocolate frosting or marmalade.