Prep ingredients: Preheat oven to 450°F with a rack in the lower third. Trim ends from Brussels sprouts, then halve through the core (or quarter, if large). Scrub potatoes, then cut into ¾-inch pieces. Scrub carrots and cut crosswise on a diagonal into ½-inch slices. Finely grate 1 teaspoon garlic.
Roast veggies: On a rimmed baking sheet, toss Brussels sprouts, carrots, and potatoes with 3 tablespoons oil; season with salt and pepper. Roast on lower oven rack until starting to brown on the bottom, 15–20 minutes.
Prep chicken: Meanwhile, in a medium bowl, whisk together harissa spice blend, all but ¼ teaspoon grated garlic, 1 tablespoon oil, and ½ teaspoon salt. Pat chicken dry then add to the bowl with spice paste. Toss to coat, massaging spice paste into chicken. Once vegetables have roasted for 15–20 minutes, add chicken to baking sheet with vegetables.
Roast chicken: Roast on lower oven rack until chicken is cooked through and vegetables are browned and tender, about 15 minutes more.
Make sauce: Meanwhile, in a small bowl, combine sour cream with remaining ¼ teaspoon garlic and 1 tablespoon water. Whisk until sauce is smooth and pourable, thinning out with more water if needed. Season to taste with salt and pepper.
Finish & serve: Remove mint leaves from stems. Discard stems; coarsely chop leaves. Drizzle sour cream over roasted chicken and vegetables and garnish with chopped mint leaves. Enjoy!
