Preheat the oven to 350 degrees F. Butter and flour a 10-inch springform pan.
Add the egg yolks and sugar to a bowl and beat with a hand mixer until light and fluffy.
Pulse the almonds in a food processor until coarsely ground.
In another bowl, whisk together the flour and leavener.
With a rubber spatula, fold the almonds and grated carrots into the egg yolk-sugar mixture; fold the flour mixture in.
In a separate bowl, combine the egg whites and a pinch of salt and beat to stiff peaks with a hand mixer. Fold the egg whites into the batter in three additions. Pour the batter into the prepared pan and bake until golden, about 1 hour. (Carrot cakes tend to be very moist, even when fully baked; so the toothpick test is unreliable. Color is a better indicator of doneness.)
Remove the cake from the oven and let cool for at least 30 minutes before removing the sides of the pan. Dust with powdered sugar right before serving.
For best flavor, let the cake sit overnight before serving.