In the bowl of a stand mixer, mix eggs, oil, vinegar and honey. In another bowl, mix all ingredients except yeast. On low, slowly mix dry ingredients into wet. It will become very dry with clumps.
Once all incorporated, slowly add club soda slowly until completely incorporated. Add yeast, beat until smooth. Once smooth, up the speed to medium-high and beat for 4 minutes.
Fill pastry bag with dough. Cut off tip so you have about a 1" opening. Squeeze the dough into circles, starting on the outer edge and working to the center. Do not over fill or they will be too tall.
Important step: Once all laid out, use a pastry brush dipped in water to help shape dough and smooth bun sides.
Let dough rise in warm, draft free place for 20 minutes, uncovered.
Bake in 375° pre-heated oven in the top 1/3 of the oven, approximately 20 minutes, until golden brown all over. (Cook to 210° internal temp. for perfect every time.) When cool enough to handle, flip out of pan and cool on a rack. This will prevent moisture from building on the bottom while cooling. Let cool completely before cutting. Use a serrated knife to cut apart and split in half. Use the day they are baked or store in a plastic bag on counter for the next day. Freezing is not recommended.
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