Preheat your grill or stovetop skillet. Season 1 pound ground chuck with ½ teaspoon salt and ½ teaspoon black pepper, and mix well. Shape beef into 4 burger patties.
Grill burger patties over medium-high heat until one side is seared well, about 3-5 minutes. If the burgers stick when you try to flip them, allow them to sear another 30 seconds to a minute until they come up easily.
Flip burgers and sear the other side about 3-5 minutes or until the burgers are done to your liking. 3 minutes on each side will cook a medium-rare burger if adding cheese. Without cheese, cook 4 minutes for a medium-rare burger.
Top each burger with 2 slices (or more, to your liking) of smoked Gruyere cheese and cook until it melts. Remove the burgers and let rest 5-10 minutes. While the burgers are resting, poach the eggs according to our guide in the post above. Alternatively, you can fry an egg instead.
While the eggs are poaching. toast the burger buns if you like your buns toasted. Caramelize onions.
When the eggs are ready, place a burger on each bun bottom. Top with a heaping spoonful of caramelized onions and a poached egg. Place top buns on top of each egg – carefully! Serve with lots of napkins, and enjoy!