Heat the olive oil in a large skillet over medium-low heat (the mushrooms are less likely to stick if you add both tablespoons, but feel free to go lighter and add more if needed). Add the mushrooms and cook for 5 minutes, stirring, until tender. (If at any point a brown coating forms on the bottom of the pan and looks like it might burn, add 1 tablespoon of water and scrape up the bits, stirring into the mushrooms). Turn the heat up to medium and add 2 tablespoons of soy sauce, stirring to coat the mushrooms. Once the liquid is fully absorbed, remove from the heat and set aside.
In a large bowl, whisk together the remaining soy sauce, miso paste, toasted sesame oil, lime juice, honey, mint, and scallions.
Bring a large pot of water to a rolling boil, and cook the soba noodles according to package instructions (typically about 4 minutes). Before draining, use a ladle or liquid measuring cup to reserve some of the pasta water. Drain the noodles, then add them to the bowl with the sauce. Gently toss to combine, adding 2-3 tablespoons of the pasta water to thin out the sauce consistency.
Divide the soba noodles into 4-6 serving bowls. Top each bowl with mushrooms, a few torn mint leaves, and a sprinkle of sliced scallions.
I've found that some brands of white miso can be a bit lumpy when mixed with other ingredients. If this happens, you can press the sauce through a fine mesh strainer before adding the noodles.