Melt the butter in a medium skillet, pre-heated medium.
Add the thinly sliced onions to the melted butter and cook for 5 minutes until they wilt. Add the thyme, salt, and pepper and cook for another 10 minutes until they start to brown.
Add the Worcestershire sauce and cook for another 10 minutes - set aside.
Gruyere Fondue Sauce
Simmer the wine in a saucepan over medium heat for 5 minutes. Add the Gruyere cheese a little at a time until all melted - storing as you go to form a creamy sauce.
Add the nutmeg and sea salt. Keep warm until ready to assemble - consistency should be easy to pour over the burger, but not too runny. Adjust with more cheese or wine until just right.
Mix all of the burger ingredients in a large bowl with your hands until well incorporated. Form into patties and press your thumb in the middle of each to indent for even cooking.
Pre-heat grill pan to medium and spray lightly with olive oil spray. Fry until the burgers are done - about ten minutes. Flip only once and do not press down.
Assemble as follows - On bottom of low-carb burger bun, spread a dab of Gruyère fondue sauce. Follow with a piece of lettuce. Then the burger and pour Gruyère cheese fondue sauce over the burger. Finally, place a good helping of caramelized onions on top and then add the burger bun lid.
If you are counting, add the nutrition information for a low-carb bun.