Mix all the ingredients for the patties in a large bowl and mix them thoroughly with wooden spoon or spatula until smooth and uniform. (If you find the mixture a bit too soft or wet to handle easily, you can add a bit more cheese or bread to stiffen it a bit.) Form the mixture into four round, flat patties. Sauté the patties in a sauté pan in a combination of oil and butter until they are nicely browned on both sides. Remove the patties from the pan.
Add a heaping spoonful of flour to the pan and let it cook int the fat for a minute or two. You can let it turn a light brown if you like. Then add the broth, whisking vigorously so it incorporates the flour well. Let the broth come to the simmer; it will thicken up a bit. Then add the cream, mix well, and add back the patties.
Let the whole dish simmer for 10-15 minutes, until the sauce has reduced considerably and the patties are done through. A few minutes before serving, add a splash of sherry and some chopped parsley to the sauce.
Serve your hamburgers immediately, with the sauce napped on top and some nice crusty bread or a few steamed baby potatoes on the side.