Heat a large skillet or grill pan over medium-high heat. Mix ground beef with salt and pepper in a bowl. Be careful not to over-mix. Form into four patties.
1 pound ground chuck, ½ teaspoon salt, ½ teaspoon black pepper
Cook burger patties over medium-high heat until one side is seared well, about 3-5 minutes.
Flip burgers and sear for another 3-5 minutes, or until the burgers are done to your liking. Check with a meat thermometer and using my beef temperature chart.
Top the burgers with 2 slices of cheese each and cook about 1 minute until melted. Set the burgers aside to rest for 5-10 minutes.
8 slices smoked Gruyere cheese
Crack the egg into the skillet after removing the burgers, and cook until done to your preference.
4 eggs
After removing the egg, rest the burger buns inside-down in the pan and toast for about 2-3 minutes or until nice and crisp if desired.
4 burger buns
If you're using caramelized onions for your burgers, reheat them over gentle heat on the stove. If you want to caramelize onions at the same time as your burgers, set a separate pan to the side in Step 2 to cook them at the same time. See: caramelized onions recipe.
Prepared caramelized onions
When the eggs are ready, place a burger on each bottom bun. Top with a spoonful of caramelized onions and a fried egg. Place the top buns back on the burger, serve, and enjoy!
Notes
Prepare the caramelized onions before the burgers to have them ready ahead of time.
Don't move the burgers around while they cook. If they're sticking to the skillet, they aren't ready to flip.
Allow the burgers to rest 5-10 minutes after cooking for best results.