Preheat oven to 400 degrees F. Meanwhile, in a large bowl, combine sweet potatoes, carrots, onion, and garlic. In a small bowl, whisk together orange juice, butter, oil, salt, and all spices. Pour over vegetables and toss to coat.
Transfer to a roasting pan and roast until a knife easily pierces the thickest pieces, 35 to 45 minutes. Increase oven to broil and cook until crisp, 3 to 5 minutes. Top with mint and Savory Roasted Pecans before serving.
To make the pecans: Preheat oven to 350 degrees F. Meanwhile, in a small bowl, combine kosher salt, freshly ground black pepper, red pepper flakes, chili powder, sweet paprika, and ground cumin; set aside. In a medium skillet over medium heat, melt butter. Add pecans and toss to coat. Add reserved spices and toss to coat. Spread nuts on a baking sheet and toast for about 10 minutes.