1. Cook the ramen noodles according to package instructions, then drain and let cool.
2. In a mixing bowl, beat the eggs and add the cooled noodles. Mix well.
3. Divide the noodle mixture into 4 equal parts and shape them into buns. Wrap each bun in plastic wrap and refrigerate for 15 minutes.
4. Heat the vegetable oil in a frying pan over medium heat. Cook the noodle buns until golden brown and crispy on both sides, about 3-4 minutes per side.
5. In another bowl, mix the ground beef with soy sauce, salt, and pepper. Form into 4 patties.
6. Cook the patties in the same frying pan over medium-high heat until desired doneness, about 3-4 minutes per side. Add cheese slices if using.
7. Assemble the burgers by placing a beef patty between two noodle buns. Serve immediately.