Preheat a pan over medium high heat and melt butter in the pan. Once the butter is melted, add your onion to the pan and lower heat to medium low. Sprinkle a pinch of salt over the onions and stir them every 2 minutes or so. You want your onions to become translucent, and then begin to change color to an amber color. If they begin to char, lower heat a little bit and stir more often. It will take about 15 minutes to get the onions to the point where they are caramelized.

In the meantime, combine all the other ingredients in a large bowl. Mix them together well, and then begin to shape the mixture into a ball. Grab the ball and throw it into the bowl from about 2-3" above. Repeat this process as your onions caramelize. You will see the texture of your mixture begin to look more homogenous (see picture above), and the mixture will stick to itself and hold it's shape without crumbling. Once the onions are done, add them to the mixture. Work them in quickly and throw the mixture for another minute or so to recover the smooth texture. Separate into four sections and shape into burgers.

Heat up your grill to medium high heat (375F-400F). Add your burgers to the grill and do not flip until at least 3 minutes, so you can get a good sear. After three minutes, flip and cook until they are to your desired temperature about 3-10 more minutes (Medium rare ~135F, Medium ~145F, Well Done 160F). Remove from the heat and rest for 5 minutes before assembling and garnishing to your liking. Enjoy!