Heat 1 tablespoon olive oil and 1 tablespoon of butter in a large soup pot over medium-high heat. Add the mushrooms. Sauté until golden, about 4 minutes. Remove and set aside so that they retain the color, flavor, and texture.
Slice the chicken in half lengthwise to create 2 thinner slices. Cover with saran wrap and use the textured side of a meat mallet to pound it to ½ inch thick.
Pat the chicken dry and season each side with salt and pepper.
Heat remaining olive oil and butter in a large soup pot over medium-high heat. Sear the chicken in batches for 4-5 minutes per side, until a golden crust has developed. Set aside turn the heat off. Let the chicken rest for 10 minutes, then cut into strips of desired size.
Add the wine and set the heat to medium. Use a silicone spatula to “clean” the bottom and sides of the skillet. Let the wine bubble gently and reduce by half, 4-5 minutes.
Add the butter and garlic and cook for 2 minutes.
Add the chicken broth, soy sauce, hot sauce, honey, sesame oil, and soup seasonings. Bring to a gentle boil and let the broth reduce and concentrate for 10 minutes while you soft boil eggs for serving (see notes for instructions).
Bring the soup to a more rapid boil, add the Ramen, and cook for 1 minute. Reduce to a gentle simmer and add the Bok Choy along with the cooked mushrooms and chicken. Simmer until the noodles are done, about 3 minutes.
Transfer to serving bowls and top with green onions, roughly chopped peanuts, and a soft-boiled egg.