Put the quinoa in a small saucepan and cover with 2 cups of water. Add a large pinch of salt and pepper and bring to a boil. Cover and cook over low heat until the water has been absorbed and the quinoa is tender, about 15 minutes.
Meanwhile, in a large skillet, toast the pine nuts over moderate heat, stirring, until fragrant, about 2 minutes. Transfer to a plate. Heat the 3 tablespoons of olive oil in the skillet. Add the garlic and onion and cook over moderate heat until softened, about 5 minutes. Add the carrots and cumin, cover and cook over low heat until the carrots are just tender, about 5 minutes. Stir in the quinoa and vinegar and season with salt and pepper.
Light a grill. Drizzle the chicken with olive oil and thread onto 4 skewers. Season with salt and pepper and grill over moderately high heat, turning, until browned and cooked through, about 5 minutes total.
Mound the quinoa salad on plates. Garnish with the toasted pine nuts and mint leaves and serve the chicken skewers alongside.