Preheat oven to 375 degrees. Line a baking sheet with parchment paper.
Toss the walnuts with the brown sugar, maple syrup, cinnamon, and chili powder. Spread in an even layer on the baking sheet. Bake for 12-15 minutes until toasted and fragrant, stirring once halfway in the cooking time. Let cool.
In a small skillet, heat the olive oil over medium-low. Add the shallot and garlic and cook until soft and golden, about 2-3 minutes. Remove from heat and whisk in the apple cider, thyme, maple syrup, and dijon. Taste and adjust salt and pepper as needed (when it's cooled down a bit, please don't scald your tongue).
Add the shredded Brussels sprouts to a large bowl along with the apple, 1 cup of the walnuts, pomegranate arils, and parmesan. Pour in the dressing and toss thoroughly until combined. Transfer to a serving bowl or dish and top with additional pomegranate, walnuts, and cheese, as desired. Serve warm or at room temperature.
Keyword apple, apple cider, brussels sprouts, fall, maple, parmesan, pomegranate, salad, side dish, thanksgiving, vegetarian, vinaigrette, walnuts