How to Make It
Preheat oven to 425°F. Toss together Brussels sprouts, oil, and salt on a small rimmed baking sheet. Roast in preheated oven until golden brown and tender, about 15 minutes. Add cranberries, and toss to combine.
Combine carrots and 1 1/2 cups of the broth in a small saucepan; bring to a boil over medium. Reduce heat to medium-low, and simmer until carrots are soft and liquid is reduced to about 2 tablespoons, 12 to 15 minutes.
Transfer carrot mixture to a medium bowl. Add sweet potatoes, and mash until slightly chunky.
Heat turkey pan drippings in a small saucepan over medium. Whisk in flour, and cook, whisking constantly, 1 minute. Whisk in remaining 2 cups broth, and bring to a boil. Reduce heat to medium-low, and simmer, stirring often, until thickened, about 5 minutes. Remove from heat, and stir in herbs. Cover to keep warm.
Divide turkey, Brussels sprout mixture, and carrot mixture among desired number of plates. Pour gravy evenly over turkey. Serve immediately.