Baking – How to make fresh burger buns like Hardees

Your buns are likely sticking to the bottom of the tray. If they stick, they will expand vertically because they can't expand horizontally. They're stuck.

Dust the trays with semolina flour, rice flour, and/or fine corn meal. You can even lightly dust them with white or rye flour, but the aforementioned flours are preferable.

If you're retarding the buns, consider placing parchment paper on the tray, lightly dusting the parchment with the aforementioned flours, and then panning the buns.

You could also use non-stick Silpats or silicone mats, but that's expensive if you have to buy a lot of them.

I don't know the composition of your dough, how you are shaping them, how much you are working the dough, etc. These could contribute the problem as well. Buns are usually enriched dough (they have butter, milk, etc.) made with low-protein AP flour. They don't need a lot of gluten development or shaping. If you develop the dough too much, it'll hold something close to the original shape (in this case, of a ball of dough instead of a disc).

The stretch and fold method is great for making breads, but most buns like this are made using something closer to the Chorleywood Process (or No Time method). Instead of resting time with stretches and folds and bulk fermentation time, this method relies on combinations of dough conditioners and heavy mechanical mixing. This usually means that the dough is mixed with a relaxer such as l-cysteine and an oxidizer like ascorbic acid. The dough is fully developed mechanically and shaped immediately, then proofed and baked.

This will be very hard to achieve at home primarily due to the conditioners used. L-cysteine and it's precursor, glutathione, are both extremely potent. A batch of hundreds of pounds of dough may require less than an ounce of conditioner, so it would be virtually impossible to scale this at home. You may be able to achieve similar results using a deactivated yeast, such as brewer's yeast, or by deactivating yeast on your own. The results will be slightly different though, as the amino acid profiles will be different.

Equipment used in a professional bakery will also make an identical result harder to obtain. Bakeries use enormous mixers that can provide more power than a home mixer, as well as special pans to help hold the shape of the bun as it proofs. Professional ovens also allow much more precise control of air flow and moisture retention than a home oven.

You may be able to achieve a good enough result with an enriched dough (like challah) and some tweaking, but it will be very hard to make an identical bun.