Roast Brussels sprouts for 15-20 minutes depending on preference and thickness of your Brussels sprouts. When they're cooked, remove from oven and allow to cool slightly.
In a small bowl or a jar with a leak-proof lid, combine lemon juice, olive oil, grated garlic and salt. Shake vigorously until the mixture is emulsified -- it'll look a lighter, opaque yellow.
Toss together the roasted Brussels sprouts and arugula. Drizzle the mixture with vinaigrette and toss to coat. Sprinkle with Parmesan cheese before serving.