In a large bowl, combine the arugula, sliced beets, crumbled goat cheese, and toasted walnuts. In a small bowl, whisk together balsamic vinegar and 2 Tbsp. of olive oil. Season with salt and pepper to taste. Dress the salad with the vinaigrette just before serving to keep the arugula crisp.
In a mixing bowl, combine the cooked quinoa, beaten egg, gluten-free flour, green onions, salt, and pepper. Mix well until the mixture is cohesive. Form the mixture into small patties.
Heat a generous amount of olive oil in a skillet over medium heat. Fry the quinoa cakes for 3-4 minutes on each side, or until they are golden and crispy. Remove from the skillet and drain on paper towels. Divide the dressed salad among plates. Top each with a few slices of beet and a couple of quinoa cakes. Sprinkle additional crumbled goat cheese and walnuts over the top if desired.
Tip:
For added flavor and color, mix golden and red beets. The quinoa cakes can be made in advance and reheated in the oven for a quick assembly.