Set up your charcoal grill for medium direct heat, or your gas grill to Medium.
Fry the bacon in a non-stick skillet over medium heat until just getting crisp. Remove and drain the bacon on paper towels, but reserve the grease in the skillet.
Add the onion slices to the hot grease in the skillet, doing your best to keep them intact. Fry them until they begin to soften, then carefully flip them over. Continue frying until they just begin to brown. Remove them to a paper towel to drain, again reserving the remaining grease in the skillet.
Fry the eggs in the reserved grease (add a little vegetable or canola oil if needed) to desired doneness ("over medium" is the way I like 'em). Keep warm.
While all the frying is going on, divide the ground beef into four equal balls. Press each ball into a patty about 1/2-inch thick at the edges and slightly less in the centers. This keeps the burgers from "doming" during the grilling.
Toast the buns over the grill.
Grill the pineapple slices until slightly caramelized on each side.
Grill the burgers to desired doneness, adding the cheese slices during the last couple minutes.
Build the burgers: Place 2 slices of bacon on each bun, then a grilled pineapple slice, then the burger, the egg, the beets, an onion slice, lettuce and tomato. Add ketchup if you must. Serve with napkins... Lots of napkins.