Make Soft Boiled Eggs. I recommend doing this first and having them peeled and ready to go since the ramen cooks so quickly. Bring a pot of water to a boil. Carefully lower cold eggs into the water and keep at a gentle boil. Cook for 6½ minutes for the perfect jammy yolk or 7 minutes for a slightly firmer center.Immediately transfer the eggs to an ice bath for 5–10 minutes. Gently crack the shell all over, then start peeling from the wider end of the egg. For the easiest peel, run the egg under cold water while removing the shell. Sauté the aromatics.
Melt the butter in a large soup pot over medium heat. Add the minced ginger, garlic, and jalapeños. Cook for 1–2 minutes, stirring often, until fragrant. Be careful not to let the garlic burn.
Make the broth.
Pour in the chicken stock, soy sauce, chili garlic sauce, sriracha, brown sugar, and rice vinegar. Stir well to combine.
Simmer Broth.
Increase the heat and bring the broth to a gentle boil. Reduce the heat and simmer for about 5–10 minutes to allow the flavors to come together.
Add the chicken.
Stir in the cooked chopped chicken and simmer for another 2–3 minutes, or until heated through.
Cook the ramen.
Add the ramen noodles, discarding the seasoning packets. Cook according to the package directions, usually about 3 minutes, stirring occasionally to separate the noodles.
Finish the broth.
Stir in the sesame oil. Taste the broth and adjust as needed with additional soy sauce, sriracha, or chili garlic sauce.
Assemble the bowls.
Divide the noodles, chicken, and broth between serving bowls. Top with thinly sliced carrots, green onions, sliced jalapeños, and soft-boiled eggs. Serve.
Finish with an extra drizzle of sriracha or sesame oil, if desired, and serve immediately.