There are many fancy ways to make burgers but I like burgers made of ground beef with nothing mixed into it. My favorite is ground short rib.
One important thing is to not put salt into the ground beef or salt too early. The salt breaks down the protein fibers which then allows insoluble proteins to bind together and make the burger tougher - the opposite of steaks.
I salt and pepper the outside before I put the burger on the grill or the skillet.
The key to cooking a burger is to get a nice sear on it without losing the juice. You can reverse sear it or sear and then slow cook, but I target the inner temperature to be around 130ºF for a firm pink.
I put onion and cheese on the burger a min or so before it's done to melt the cheese and slightly cook the onion.
I toast the buns with a little butter on them and add various condiments.
Fry sauce is a family favorite.
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