I have always hand-shaped my burger buns, but after buying a set of ring molds for English muffins, I saw the opportunity to create perfectly identical buns. I took my usual burger bun dough and portioned it into a dozen round balls. I then lightly oiled the inside of each ring mold and placed them on a parchment-lined baking sheet.
It quickly became apparent that each ball was far too small to fill the ring mold, so I took a slightly oiled plastic bench scraper and flattened each ball into a disc, placing one in the center of each ring. I let the dough rise for a bit over an hour, brushed the tops with egg wash, then baked as per usual.
The buns did indeed generally fill the rings. Though it would be a bit generous to say they were all identical, they were at least the same diameter. Furthermore,the cylindrical base (while a bit odd looking), did make them a bit easier to split by providing some landmarks.
I’m not sure the technique worth the effort for burger buns, but it could prove useful for ensuring a fixed size when needed.