Preheat oven to 350 degrees F (175 degrees C). Brush three pastry rings with olive oil, place them on a baking sheet lined with parchment paper and set aside.
In a small bowl, beat egg whites until soft peaks form, set aside. In another small bowl, whisk together egg yolks and olive oil, set aside.
In a medium bowl, combine almond flour, buckwheat flour, dark flaxseed meal, caraway seeds and salt. Stir egg yolk mixture and egg whites into flour mixture until just combined, a few small lumps are fine.
Pour batter into the prepared pastry rings and sprinkle tops with caraway seeds. Bake 15 to 18 minutes or until bun is firm when touched. Cool buns on baking sheet to room temperature. To remove buns from pastry rings, run a sharp knife along the inside of rings.
To serve, slice buns in half with a serrated knife.
Buns are best if eaten within a day or two, but will keep in an airtight container on the counter for up to a week. Buns can also be frozen.
If you don’t have pastry rings, you can use tuna or pineapple cans (labels removed) that have been washed, dried and both top and bottom lids removed.