Bring 2 cups water to a boil in a small saucepan. Add the quinoa, season with salt and cover. Reduce the heat to a simmer over medium-low, and cook until the quinoa has absorbed the water, about 15 minutes. Remove from the heat.
Meanwhile, in a small bowl, mix together 2 tablespoons of the olive oil, the chipotle powder, oregano and 1 grated garlic clove. Season the mixture with salt and pepper. Sprinkle the chicken breasts on both sides with salt and pepper and rub the chipotle mixture evenly over the meat.
Heat 1 tablespoon of the olive oil in a large heavy skillet over medium-high heat. Add the chicken breasts and cook, turning once, until browned and cooked through, about 5 minutes per side. Remove from the heat, cover, and let stand for 5 minutes before slicing.
In a small bowl, whisk together the lemon juice, Dijon, shallots and remaining grated garlic until combined. While whisking, slowly drizzle in the remaining 1/2 cup olive oil until thick and emulsified. Season the dressing with salt and pepper.
In a large mixing bowl, toss the cooked quinoa, kale, Brussels sprouts and almonds together until combined. Add the dressing and cheese and toss lightly until coated; season with salt and pepper.
Divide the mixture among 4 serving plates and top each with a sliced chicken breast. Serve immediately.