Bring water to a boil in a pot. Rinse swordfish and pat dry; season both sides with a pinch of salt and pepper. Reduce boiling water to a simmer. Stir in bouillon and 3/4 of the lime juice. Add carrots, bean sprouts, soy sauce, green onions, jalapeno, lemongrass, cilantro, 2/3 of the garlic, and ginger. Simmer broth for at least 10 minutes.
Heat 1 tablespoon olive oil in a saucepan over medium heat. Add mushrooms; season with a pinch of salt and pepper and add remaining garlic. Cook until tender, about 5 minutes. Transfer mushrooms to a bowl. Wipe the pan clean if there are bits stuck to the bottom.
Return pan to medium-high heat; add remaining olive oil and swordfish. Cook until internal temperature reaches at least 145 degrees F (63 degrees C), 4 to 5 minutes per side. Squeeze remaining lime juice over the fish and set aside to rest.
Add mushrooms and bok choy to the broth. Continue simmering on low, about 5 minutes. Add soba noodles; cook until heated through, 5 to 7 minutes. Add sesame oil.
Cut each block of noodles in half and divide between 4 bowls. Ladle vegetables and broth over the top. Cut swordfish steaks into equal pieces and place one on top of each bowl.
