In a large mixing bowl, add the flours, flaxseed powder, psyllium husk powder, salt, and baking powder.
Whisk until well combined, then add the eggs, egg whites, water, and oil. Mix until all of the flour is incorporated and you have a wet dough.
Cover with plastic wrap and allow to sit for at least 45 minutes to allow the flours to absorb the moisture.
Preheat the oven to 350°F (180°C). Line a baking sheet with parchment paper.
Divide the dough into two pieces for larger buns or four pieces for slider buns.
Mold the dough into rough bun shapes with flattened bottoms and slightly domed tops, then place on the baking sheet. Keep in mind that the dough won’t rise or spread very much, so try to shape the dough to the size of your burger patty.
Slice the tops of the buns about ¼ inch deep so that air can escape while baking, then sprinkle with sesame seeds.
Bake the buns for 35-40 minutes until slightly golden and firm.
Remove from the oven and allow to cool completely before slicing.