Start by thinly slicing one large onion. In a skillet over medium heat, add a tablespoon of butter. Once melted, add the sliced onions. Cook them slowly, stirring occasionally, until they become soft and golden brown, about 15-20 minutes. Set aside.
In a mixing bowl, combine the ground beef, Stone House Seasoning, and Worcestershire sauce. Form the mixture into two equal-sized patties, about ½ inch thick.
In the same skillet used for the onions, add a tablespoon of butter over medium-high heat. Once hot, add the patties to the skillet. Cook for about 4-5 minutes on one side, then flip and cook for another 4-5 minutes, or until they reach your desired level of doneness. Place a slice of sharp Cheddar cheese on each patty during the last minute of cooking to allow it to melt.
Spread a tablespoon of softened butter on one side of each slice of sandwich bread. On the unbuttered side of four slices, layer the melted patties with the sharp Cheddar cheese, a generous amount of caramelized onions, and a slice of mild Cheddar cheese. Top with the other slices of bread, buttered side facing out.
In the same skillet, add the assembled sandwiches. Cook for about 3-4 minutes on each side, until the bread is golden brown and crispy, and the cheese is gooey.
Remove the sandwiches from the skillet and let them cool slightly. Cut in half and serve with your favorite sides, like crispy fries or a fresh salad. Enjoy!