This question seems a bit odd, given that all it requires is a recipe for a bakery that produces one of the most famous, and appetizing buns for burgers, for a restaurant known as In-N-Out burger. So I will tell you what I have been able to gather from research on the recipe, and what makes it possible for these buns to be spongy, instead of the regular buns used by most restaurants in burgers.
According to an article placed by In-N-Out burger, the buns are made by a small bakery known as Puritan Bakery and they do not sell to individual consumers but only to restaurants. In-N-Out has become famous rather for using these buns. The difference in them lies in the fact that they are spongy, which is not a characteristic of most burger buns.
The recipe simply states that what they do to accomplish this is to first make a combination of water, yeast, flour and instead of using butter, or oil, they use an element called shortening. After that first process, they let the dough rest for an entire night in a special pan. Afterwards, they take the dough and add the rest of the ingredients, and more flour. Apparently, the fact of mixing the ingredients in a first step with shortening, allows the sponge to form, thus making these buns so characteristic.
