Without flour or eggs
The ground-meat hamburger is as ubiquitous as the letter ‘M’. At home, the texture of hamburger mince mostly depends on the binding agent. Eggs, flour, breadcrumbs and/or milk are often used to bind, however these agents either don’t bind, are poor binders, or interfere with binding. The most effective binding agent is salt. It is worth understanding this process so that it can be manipulated to get the result you like.
When meat is ground (or cut), meat protein (myosin) begins to leak out. This process can be accelerated by adding salt, which draws moisture from the meat and the myosin with it. Proteins are the building blocks of gels. First the protein gets hydrated, then under heat it unravels and entangles, trapping moisture and setting. This is how other heat-set protein gels, such as scrambled eggs, form. The myosin gel will bind nicely to itself and to the protein on the surface of the mince, and thus hold everything together.
The amount of salt will determine both taste and texture. In both cases, less is better. The maximum to try would be 2% salt (by weight of mince), and 5% water (iced). Alternatively, replace the water with stock or other flavoured liquid (unsalted). Knead it a while. A nice mince mix is 50:50 pork and veal.
There are some that would argue no salt should be added to hamburger mince at all, so as to achieve maximum looseness of texture. The patty will become firmer as more salt is added (and myosin released). The myosin gelation can be broken down by adding other ingredients that interfere with the process.
I suspect that the real contribution of an added egg, for example, is not the egg itself, but the water content of the egg, which helps the myosin gel. The egg proteins will set of course, although they set lightly and I’m not sure they really bind to the meat. Breadcrumbs (and diced vegetables) will get in the way of gelation. Milk will contribute water, although the fats in milk will interfere with gelling. Flour just adds glug in my opinion (except to crisp the outside).
