Add the olive oil to a large stockpot set over medium heat. When hot, add in the scallion whites, the carrot and the mushrooms. Cook for about 5 minutes, until softened. Add in the garlic and ginger, and cook for 30 seconds to 1 minute, until fragrant. Add in the broth, soy sauce and the bok choy stems. Bring the mixture just barely to a boil, then reduce the heat and simmer for 15 minutes.
Add in the the ramen noodles and bok choy leaves. Continue to simmer, adjusting the heat as needed, for about 4 to 6 minutes, or until the noodles are just tender. Remove from the heat. Carefully ladle a scoop of the broth into a small bowl. Add in the miso paste and whisk to combine. Add the mixture back to the pot and stir to combine. Taste and adjust seasonings as desired.
Serve the ramen topped with the scallion greens, sliced jalapeño and soft boiled eggs.