Season the ground beef with salt and pepper, knead to mix then flatten into two patties. Make a slight dimple in the middle of each with your thumb (this helps it be flatter rather than thicker in the middle when it cooks). Chill the patties while you prepare other ingredients and warm the grill (barbecue) or a grill pan.
Cut the tomato into slices and slice the burger buns through the middle, if not already cut. If you like, you can shred the lettuce or leave as a whole leaf, as you prefer.
Lightly toast the buns on the inside side (you can do the other side too, but less needed). At the same time, lightly grill the pineapple on both sides to give light grill marks. Both will only take a minute or two, so keep a relatively close eye.
Set the buns and pineapple to one side, ideally keeping them warm, then cook the bacon and the burgers. If cooking on a grill, watch as fat dripping can cause flames and it can easily burn, so can be best to cook in foil rather than directly on the grill.
Shortly after you turn the burger to cook on the second side, add the cheese on top of the cooked side to let it melt as the second side cooks. Remove the burgers and bacon once cooked.
As the burger is cooking (or if not able to do at the same time, after and keep the rest warm), warm the oil over a medium-high heat and fry the eggs. You ideally want the yolk soft but the white cooked and lightly crisp on the underside.
Spread mayonnaise on the bottom side of the buns, and some barbecue sauce on the top half.
Layer up the burgers: onto the bottom bun add lettuce, a slice or two of tomato, a pineapple ring, a slice of beet, the burger, egg then bacon. Top with the other half of the bun and, if needed (almost definitely!), use a cocktail stick to hold it all together.