Adjust oven rack to upper-middle position and heat oven to 500 degrees. Toss Brussels sprouts, 3 tbsp oil, water, ¾ tsp salt, and ¼ tsp pepper in a large bowl until sprouts are coated. Transfer sprouts to rimmed baking sheet and arrange so cut sides face down. Cover sheet tightly with aluminum foil and roast for 10 minutes.
Heat remaining 3 tbsp of oil in 8-inch skillet over medium heat until shimmering. Add garlic and red pepper flakes; cook until garlic is golden and fragrant, about 1 minute. Remove from heat.
Remove foil and continue to cook until Brussels sprouts are well browned and tender, 10 to 12 minutes. Transfer to serving platter, toss with garlic oil, and season with salt and pepper to taste. Sprinkle with Parmesan and serve. Serves 6 to 8 as a side dish.