Make ramen “buns”: In a large pot of salted boiling water, cook ramen according to package instructions. Drain and rinse noodles with cold water.
In a large bowl, toss noodles with eggs until evenly coated. Season with salt and pepper.
In a large nonstick pan over medium heat, pour enough vegetable oil to thinly coat the bottom of the pan. You can get creative here to make the mold for the Ramen buns. You can make a plastic-wrap-lined mold the same size as you want your burgers to be (4-5″ across). Fold the plastic wrap back over the noodles and place a weight on top to compress as they cool. Or use the rings of 4 mason jar lids in the pan. Using tongs, fill each ring with the noodle mixture, then press down on each to make the noodles more compact. Cook until golden, about 4 minutes per side. Repeat, then wipe pan clean.
Make burgers: In a large bowl, combine ground beef, jalapeño, onion, green onion and garlic powder. Slice the scallions and mix into the beef with the noodle seasoning, soy sauce, and sesame oil. Form two burger patties, a similar size to your buns, keeping them pretty thin. Mix until just combined. Form the mixture into 4 patties, then season both sides of each patty with salt and pepper.
Return pan to medium-high heat and pour a thin layer of oil to coat the bottom of the pan. When the oil is hot, add the beef patties. Cook until the meat is cooked to your liking, about 4 minutes per side for medium. For the last minute of cooking, top each patty with a slice of cheese. Cover the pan with a tight-fitting lid and cook until the cheese is melted, about 1 minute.
Assemble burgers: Top 4 of the ramen buns with lettuce, tomato slices, and burger patties. Drizzle with Sriracha, if desired, then top with remaining ramen buns.