1. Gather all the ingredients for the classic patty melt, including ground beef, rye bread, Swiss cheese, an onion, butter, vegetable oil, salt, and pepper.
2. Form the ground beef into a thin, oval-shaped patty slightly larger than your bread slices. Season both sides with salt and pepper.
3. Heat 1 tablespoon of butter in a skillet over medium-low heat. Add the sliced onion and cook slowly, stirring occasionally, until caramelized and golden brown (about 15-20 minutes). Remove the onions from the skillet and set aside.
4. In the same skillet, increase the heat to medium-high, add vegetable oil, and cook the seasoned beef patty for 3-4 minutes on each side until cooked to medium doneness. Remove the patty from the skillet and set aside.
5. Butter one side of each slice of rye bread. On the unbuttered side of one slice, place one slice of Swiss cheese, then add the cooked beef patty, followed by the caramelized onions, and another slice of Swiss cheese. Top with the second slice of bread, buttered side facing outward.
6. Wipe the skillet clean and return it to medium heat. Place the assembled sandwich in the skillet and cook for 3-4 minutes on each side. Press gently with a spatula to ensure the bread gets golden brown and crispy while the cheese melts fully.
7. Once done, remove the patty melt from the skillet and let it rest for one minute.
8. Cut the sandwich diagonally and serve immediately, paired with your favorite sides like French fries, onion rings, or a pickle spear.
9. Enjoy your delicious, homemade patty melt!