Leftover buns can be stored, loosely covered, at room temperature for up to 1 day. After that, they can be frozen in a freezer-safe baggie for up to 3 months.
Xanthan gum or psyllium husk powder can be used, however, the psyllium husk powder will result in a slightly denser, whole-wheat type bun.
If using psyllium, be sure to use psyllium POWDER, not whole psyllium husks! Powdered psyllium and whole psyllium husks measure very differently so they are not interchangeable.
While adding sweetener is optional, it gives the buns a slight sweetness similar to traditional hamburger buns. For the sweetener, any erythritol-based sweetener will work. If you're paleo, feel free to use coconut palm sugar.
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For grain-free baking powder, combine 1 part baking soda with 2 parts cream of tartar and 2 parts starch (such as tapioca, arrowroot, or potato).