In a large skillet over medium heat, add the ground beef, salt, black pepper, and crushed red pepper. Cook, breaking up the meat, until browned, about 8 minutes.
Drain the excess grease.
Add the garlic and cook for 1 minute.
Reduce the heat to low. Stir in the chili garlic sauce and rice wine vinegar. Remove from heat and cover to keep warm.
For the Soft-Boiled Eggs
Bring about 2 inches of water to a boil in a small saucepan.
Gently add the eggs and boil for 6 minutes.
Transfer the eggs to an ice bath to stop cooking. Once cool enough to handle, carefully peel and set aside.
For the Noodles and Assembly
Bring 4 quarts of water to a boil in a large saucepan.
Add the ramen noodles (reserve the flavor packets) and cook for 3 minutes, or until tender.
Reserve 1 cup of the noodle water, then drain the noodles.
Add the reserved water, flavor packets, and cooked noodles to the skillet with the beef mixture. Toss until well combined.
Divide into 6 bowls. Top each with sesame seeds, green onion, and half a soft-boiled egg. Serve warm.