Combine the pear, Spanish onion, garlic and ginger in a food processor and puree until smooth, approximately 1 minute. Transfer to a large bowl.
Add the sliced beef and toss, using tongs to coat well. Marinate for at least 10 minutes.
Add the soy sauce, sugar, gochugaru and sesame oil then toss together. Cover and refrigerate for at least 30 minutes.
Bring a pot of water to boil. Add the noodles and boil for 5 minutes, until tender and chewy. Drain and rinse in cold water.
Cut noodles a few times with a kitchen scissors and toss with soy sauce and sesame oil. Cover and set aside.
Transfer the marinated beef, along with the sauce into a large skillet. Spread the scallions, Vidalia onion, carrot and mushrooms on the top of the meat.
Place the skillet over high heat. When the beef and sauce starts bubbling, turn and stir the meat and vegetables with the noodles using tongs. Add marinated noodles. Cook until the beef is no longer pink and the noodles are translucent, approximately 5-6 minutes.
Transfer cooked bulgogi, noodles and vegetables to a serving plate and serve hot. Sprinkle with sesame seeds.