Preheat the oven to 400 degrees F.
Cut the stems off of the brussels sprouts and cut each in half.
Remove the skin from the butternut squash and cut into small cubes (about 1-inch).
In a large bowl, combine the brussels sprouts, squash, mushrooms, and pine nuts. Add the olive oil, salt and pepper and toss until the vegetables are evenly coated.
Arrange the vegetables in an even layer on a large baking sheet and bake for 40-45 minutes, tossing halfway through.
While the vegetables are cooking, combine the tahini and garlic to make the dressing.
When done, remove the vegetables from the oven and toss with dressing before serving.