In a large pot, bring the vegetable broth and water to a boil. Add the instant ramen noodles and cook according to package instructions until just tender. Drain and set aside.
In the same pot, melt the butter over medium heat.
Add the minced garlic and red pepper flakes to the melted butter. Sauté for about 1-2 minutes until fragrant, being careful not to burn the garlic.
Pour in the soy sauce and sesame oil, stirring to combine the flavors.
Add the chopped bok choy to the pot and cook for about 2 minutes until wilted.
Toss the cooked ramen noodles back into the pot, stirring well to coat them in the spicy garlic butter sauce. Let everything cook together for another 1-2 minutes to absorb the flavors.
If desired, in a separate pan, lightly boil or poach the eggs to your preferred doneness (soft-boiled is recommended).
Season the ramen with salt and pepper to taste before serving.
Serve the ramen in bowls, topped with sliced green onions and the prepared eggs if using.
Notes
Adjust red pepper flakes based on your spice preference.