For the dressing: Mix the oil, red wine vinegar, Dijon mustard and shallot in a small bowl; set aside.
For the roasted beet salad: Preheat the oven to 350 degrees F.
Wash the beet on and roast it on a rimmed baking sheet until tender, about 1 hour. Cool and peel; set aside.
Cook the quinoa according to the package instructions. Cool and set aside.
Slice the beet about 1/8-inch thick. Mix together the quinoa, chicken and spinach in a large bowl. Season lightly with salt and pepper and then add enough dressing to lightly coat. Add the sliced beets and place on a plate. Top with the goat cheese.