Wash Brussels sprouts and peel off any wilted or browned outer leaves. Trim the base of each Brussels sprout, then cut into quarters length-wise. Wash shiitake mushrooms, trim off stems (save stems for vegetable stock or other use later). Cut shiitake mushrooms into roughly the same size as the Brussels sprouts quarters. For small/baby shiitakes, cut caps into halves; for larger shiitake mushrooms, cut caps like you would a pizza, into quarters.
Heat grapeseed oil in large pan over medium heat. When hot, add the Brussels sprouts, turning the quarters so one of the cut sides faces down. Allow to cook until starting to brown, about 3 minutes, then turn each Brussels sprout so the other cut side is down. Allow to cook for another 3 minutes.
While the Brussels sprouts are cooking on their first side, whisk together the miso, rice vinegar, maple syrup, and minced garlic in a small bowl. Set aside.
Turn the heat under the pan to medium-high. Add the shiitake mushrooms to the pan with the Brussels sprouts. Cook while stirring so the shiitake mushrooms do not stick to the pan. Once the shiitake mushrooms are browned and the Brussels sprouts are just starting to char, remove the pan from the heat. Pour in about half the miso mixture and stir to coat the Brussels sprouts and shiitake mushrooms. Taste a Brussels sprout. Add more miso mixture if necessary. Season with salt to taste. Miso is salty so you may not need any salt.
Transfer Brussels sprouts and shiitake mushrooms to large shallow serving bowl (or serve straight from skillet). If you are using chili pepper or togarashi for heat, sprinkle over Brussels sprouts and shiitake mushrooms.