Fill a small saucepan with enough water to cover eggs and bring to boil over high heat. Reduce heat to medium and slowly lower eggs into boiling water with a slotted spoon (to avoid cracking). Reduce heat to simmer and cook 7 minutes (or longer if you prefer firmer yolks); transfer eggs to ice bath for 5 minutes or more. (See recipe note.)
Meanwhile, heat butter in a medium nonstick skillet over medium heat until melted and sizzling. Add shrimp; cook and stir 3 minutes or until just cooked through (do not overcook). Remove from heat.
Bring chicken broth to boil in a medium saucepan.
Add ramen noodles to boiling broth and cook 1 minute. After 1 minute, add ginger, garlic and bok choy; bring to boil and cook 2 minutes more, or until noodles are tender. Add shrimp and and accumulated juices and stir to heat through. Remove from heat and stir in soy sauce and sesame oil. Taste for salt and add more soy sauce as desired.
Divide noodles, shrimp and bok choy evenly between two bowls. Peel and cut eggs in half lengthwise. Top each bowl with two egg halves and desired amounts of sriracha and green onions. Serve.
Notes
Confession: I don't always wait the full 5 minutes. If the soup is ready and I've just transferred the eggs to an ice bath, I peel them right away and it works well. Just be a bit gentle when cracking the shell and peeling.