Let the meat get as close to room temperature as you can manage. Prep everything. Slice cheese, then tomatoes and onions into 1/2" thick slices, and lay out buns, lettuce, pickle and anything else.
Heat grill to high, or at least 400 degrees F.
Whisk egg in a bowl and combine everything but the meat. Add the meat and stir with your hands to evenly distribute without overmixing.
Divide the pound of meat into 3, then shape into patties almost an inch thick. Gently press your thumb into the center to make a light indentation, which should reduce puffing while they cook.
Salt, Pepper, and splash oil on each side and around the rim of the patties, then place them on the grill. Close lid and grill until no longer pink inside, turning once, about 6 – 8 minutes per side. When you flip them, baste them with room temperature butter. When you have about a minute remaining, add cheese if desired. Don't poke or move the patties at all, except to flip them once.
If grilling onions, take your 1/4" slices of onion and add salt, pepper and oil to each side, then put them on the grill right when you add the meat. Flip the onions when you flip the burgers. Toast the buns in the same way, with salt pepper and a little oil.
Just before taking them off the grill, throw on a touch more salt and pepper to season the outside since the rest has worked it's way inside the meat.
Spread mayo and mustard in a thin layer on the inside of each bun. On the base, add lettuce, tomato, another sprinkle of salt and pepper and a touch more mayonnaise/mustard, then the patty, then the top bun. Use a toothpick to keep it together.
