Divide 1 lb ground beef into 4 equal portions and roll each portion into a loose ball. Do not form into patties. Refrigerate the beef balls while you prepare the vegetables and other ingredients.

Slice the yellow onion and red onion. Slice the red pepper and yellow pepper. Slice the avocado and set aside.

Preheat one area of the griddle to medium (about 350–375°F). Add 2 tbsp salted butter and spread it across that area.

Add the sliced onions and peppers to the buttered area of the griddle. Season the vegetables with salt and pepper (to taste). Cook, flipping every couple minutes, until softened and lightly caramelized. If the vegetables start to stick or burn, add the optional 1 tbsp avocado oil sparingly as needed.

When the vegetables are done, move them to a cooler section of the griddle or off the heat. Leave the burner on low (or turn it off) and keep the vegetables on the griddle to stay warm while you cook the burgers.

Preheat another area of the griddle to high (about 500°F). Add the second 2 tbsp salted butter and spread it across the high-heat area.

Place the chilled beef balls onto the hot, buttered griddle area. Immediately press each ball into a thin patty using a burger press or a large metal spatula. If using a metal spatula, place a piece of parchment paper between the spatula and the meat while smashing to prevent sticking.

After smashing, divide the 1 tsp salt and 1 tsp pepper into four equal portions and sprinkle one portion (about 1/4 tsp salt + 1/4 tsp pepper) onto each patty. Cook the patties undisturbed for about 2 minutes.

Flip each patty. Immediately place one slice of cheddar cheese on each flipped patty and cover with a steam dome (or an inverted bowl) to help the cheese melt. Cook about 2 more minutes or until done to your liking.

Remove the cheeseburger patties from the griddle and place them on a clean plate or tray.

Preheat a third area of the griddle to low (about 300°F) for toasting buns and cooking eggs. If you prefer to toast the buns in butter, you may use the buttered area where the vegetables were cooked; alternatively, use the optional avocado oil sparingly. (No additional butter amount is listed for buns.)

Split the 4 hamburger buns and place them cut-side down on the low-heat area. Toast the cut sides until golden, about 1–3 minutes. Remove and keep warm.

Add the remaining 1 tbsp salted butter to the low-heat area (or use the already-buttered surface) and spread. Crack one egg per burger onto the buttered surface and cook sunny-side-up for about 4 minutes, or until the whites are set and yolks are cooked to your preference.

Assemble each burger: place a toasted bottom bun on a plate, add a generous portion of the griddled onions and peppers, place a cheeseburger patty on top, then gently place a fried egg on the patty.

Sprinkle each egg yolk with the 1 tsp everything bagel seasoning and the 1 tsp fresh chopped cilantro.

Top each burger with sliced avocado and drizzle with the 1 tbsp hot sauce or Worcestershire sauce (use as desired). Add the top bun.

Serve immediately. Optional toppings you may also add: tomato, lettuce, etc.