In a heavy skillet over medium heat, melt 1 tablespoon of butter. Add the sliced onions, red peppers, and jalapeños.
Sauté the vegetable mixture for 15 to 20 minutes, stirring frequently to prevent burning, until deeply caramelized. Deglaze with Worcestershire sauce and remove from heat.
Divide the ground beef into two 5-ounce portions and shape into thin oval patties matching the dimensions of the rye bread.
Season both sides of the patties with salt and pepper. Sear in a hot skillet for 3-4 minutes per side until internal temperature reaches 160°F (71°C).
Wipe the skillet clean. Butter one side of each bread slice.
Assemble the sandwiches by placing two bread slices butter-side down in the skillet. Top each with one slice of Swiss cheese, one beef patty, half of the caramelized vegetable mixture, and a second slice of Swiss cheese.
Place the remaining bread slices on top, butter-side up. Griddle over medium heat for 2-3 minutes per side until the bread is golden brown and the cheese is fully emulsified.
Remove from heat, slice diagonally, and serve immediately.