Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper. If you have a light-colored sheet, use that—darker pans brown faster.
Whisk the dry mix. In a medium bowl, whisk almond flour, psyllium husk, baking powder, and salt until no lumps remain. This quick step helps the buns rise more evenly.
Mix the wet ingredients. In a separate bowl or large measuring cup, whisk the eggs, apple cider vinegar, melted butter or olive oil, and sweetener (if using). It should look silky and well combined.
Combine wet and dry. Pour the wet ingredients into the dry and stir with a spatula until you have a thick, slightly grainy dough. It’ll look dry—totally fine.
Add the boiling water. Carefully pour in the just-boiled water while stirring. The dough will absorb the water and transform into a soft, pliable, slightly tacky mass. Magic. Let it sit for 3–5 minutes to thicken further.
Shape the buns. Lightly oil your hands. Divide the dough into 6 equal portions. Roll each into a ball, then gently flatten to about 3/4 inch (2 cm) thick. Place evenly spaced on the baking sheet. If you like, brush the tops with a little water and sprinkle sesame seeds.
Bake. Slide the tray into the oven and bake for 22–28 minutes, until the tops are dry, lightly golden, and firm to the touch. If your oven runs cool, give them another 2–3 minutes.
Cool before slicing. This is the patience step. Let the buns rest on the tray for 5 minutes, then transfer to a rack to cool at least 10–15 minutes. They set up as they cool, which prevents a gummy texture.
Serve or toast. Slice horizontally with a serrated knife. For best flavor, toast the cut sides in a skillet with a touch of butter or on a grill pan. Build your burger and enjoy the soft bite and sturdy hold.