In a large pot, heat the toasted sesame oil over medium heat. Add in the onion and cook until translucent, stirring occasionally, about 5-8 minutes.
Add in the garlic and ginger. Sauté for 30 seconds then stream in the water or stock and add in the dried shiitake mushrooms.
Put the lid on and turn the heat up to high. Once it comes to a boil, reduce the heat to a simmer and cook for another 30 minutes.
Remove from heat. Over a large bowl, carefully strain the soup over a fine mesh sieve.
Place the mushrooms, onions etc that you've strained out in a high-speed blender with about a cup or so of the broth. Pour the broth back into the pot.
Add the soy sauce, mirin and miso paste to the blender. Blend on high until completely smooth.
Pour the blended mixture back into the pot, stir, and turn the heat back on to low, cover and keep warm.
In a small bowl, whisk together all of the ingredients for the marinade.
Cut the tofu into 1 inch cubes, or in small triangles.
Pour the marinade into a baking tray. Place all of the tofu onto a single layer in the marinade. Let sit for at least 30 minutes, flipping the tofu once.
Heat a stove top grill pan or a skillet over medium heat. Brush the grills with sesame oil.
Once hot, add the tofu pieces in a single layer. Cook for about 4-5 minutes per side, until heated through and some nice sear lines appear.
Grease the pan with sesame oil, and cook the shiitake mushrooms in a single layer. Cook for 2-3 minutes, flip them, and cook for another 2-3 minutes.
Pour the remaining marinade, half over the tofu and half over the shiitake mushrooms. Toss to coat.
Prepare the noodles according to package directions in a pot that is big enough to also hold the bok choy.
Two minutes before the noodles are ready, place the baby bok choy on top of the noodles to briefly cook.
To serve, ladle some broth into bowls, add noodles and then top with the tofu, shiitakes, baby bok choy, green onions and sesame seeds.
