Heat the olive oil in a skillet over medium heat. Stir in the garlic and shallots; cook and stir until the shallots have softened and turned translucent, about 5 minutes. Stir in the cumin, ginger, and cinnamon. Cook until fragrant, about 1 minute more. Add the chicken broth and quinoa, and bring to a boil, then reduce heat to low. Cover and cook until the quinoa is tender and the liquid has been absorbed, about 20 minutes.
Meanwhile, place raisins in a bowl and cover with hot water. Soak until the raisins soften and plump up, about 15 minutes. Drain and set aside.
Fluff the quinoa with a fork and stir in the lemon juice. Remove from heat and allow to cool to room temperature. Stir in the garbanzo beans, raisins, carrots, parsley, basil, and mint. Serve at room temperature or chilled.