Prep all of the vegetables as the oven comes to proper temperature.
In a large bowl, mix the Brussels sprouts, shiitake mushrooms and shallot with the olive oil, salt and pepper.
Evenly distribute the vegetables between the two baking sheets. *The key is to not overcrowd one pan.*
Separate the Brussels from the shiitake and shallots. *I like to put all of the Brussels onto one side of the baking sheet while leaving the shiitakes & shallots on the other side. The Brussels sprouts usually take longer to roast in the oven.*
Flip the Brussels Sprouts over so they are "face down". This will allow them to brown and caramelize in the oven.
Roast the veggies for 30 minutes. Carefully remove the shiitakes and shallots from the baking sheet with a spatula and check to see if the Brussels sprouts need additional time. Perhaps 5-10 more minutes. *You can give the baking sheet a shake to distribute the Brussels even more.*
While the vegetables are roasting, reduce the balsamic vinegar in a small sauce pan over medium heat. The vinegar will reduce into a thick, syrupy consistency, takes about 8-10 minutes.
Once the Brussels are caramelized and crispy, remove from the oven and toss with the roasted shittakes and shallot. Taste to see if additional salt & pepper is needed.
Add the lemon zest, freshly grated Parmesan cheese and drizzle with the reduced balsamic.
Crumbled blue cheese also works very nicely in place of the parmesan.