Start by heating a tablespoon of butter in a skillet over medium heat. Add the thinly sliced onions, red peppers, and jalapenos. Sprinkle with a pinch of salt and sauté for about 10-15 minutes, stirring occasionally, until the onions are caramelized and the peppers are tender.
In a separate bowl, season the ground beef with salt and pepper. Form it into two patties.
In another skillet, cook the patties over medium-high heat for about 4-5 minutes on each side, or until they are cooked to your desired doneness. If you like your cheese extra melty, place a slice on each patty during the last minute of cooking and cover with a lid.
On one slice of rye bread, layer a patty with melted cheese, followed by a generous scoop of the caramelized vegetable mixture. Top with another slice of bread.
Spread the remaining tablespoon of butter on the outside of the sandwich. Place it back in the skillet over medium heat. Cook for about 3-4 minutes on each side, until the bread is golden brown and crispy.
Remove the patty melt from the skillet, slice in half, and serve immediately with your favorite sides, like fries or a simple salad. Enjoy!