Cook the Ramen: Boil ramen until al dente, drain, and reserve ¼ cup cooking water.
Make the Garlic Butter Sauce: Melt butter in a skillet, add garlic, and cook until golden and fragrant. Stir in chili flakes, brown sugar, and soy sauce; simmer for 1 minute.
Toss the Noodles: Add cooked noodles and a splash of the reserved ramen water; toss to coat in the sauce.
Cook the Egg: Push noodles aside, crack in the egg, and stir gently until almost set. Mix the egg through the noodles, adding more water if needed.
Serve: Transfer to a bowl and garnish with everything bagel seasoning and green onions, if desired.