Slice 3-5 nice looking pieces of the onion for serving on the buns. Chop the rest of the onion.

Pre-heat a pan over medium heat. Add the butter/oil and heat for 1 min then add the onion. Cook on medium until translucent, around 15-20 minutes. Do not turn up the heat too much and try to rush this step. If the oil is smoking or the onions are burning and sticking to the pan, the heat is too high. If the onions start to stick you can deglaze the pan with the wine. Add the wine and turn the heat to medium/high. Watch the pan and when the liquid evaporates turn it off.

Cool the onions on a glass plate in the freezer. 15-20 minutes.

Mix the ground beef, chilled onions, salt/pepper, and Lee and Perrins Worcestershire Sauce.

Place the wax paper over a cutting board, and put the big meat ball on in the center. Form the meat into a log, and cut into 4 equal pieces. Form the burgers. Press the center if no-pink is desired.

Cook for 7 minutes on medium-high if using a stovetop pan
Or use 400* in the air fryer. Pre-heat the air-fryer for a grille like crust. Don't overcook trying to get the crust.
Grill for 8-10 minutes on medium high heat.

Notes:
Stater Bros w-sauce is not a replacement. Might as well make Ronnie Burgers.
Don't undercook it or you will be fired.