Preheat grill to medium high heat.
Heat 2 tablespoons of olive oil in pan over medium high heat and cook onions until golden brown, about ten minutes.
Add the brown rice, beets, walnuts, garlic powder and cooled onions to a food processor and pulse about 10 times, until the mixture is ground similar to ground beef.
Transfer to a bowl and add the eggs, 1 teaspoon salt and some pepper. Mix by hand until uniform, then tightly form into 4 patties.
In a small sauce pan bring ½ cup of water to a boil. Add ¼ cup quinoa, reduce heat to low and cover. Cook until all the liquid is absorbed and quinoa is tender, about 12 minutes.
Spread quinoa on a baking sheet and let cool.
Cook under the broiler on high rotating the quinoa half way through. Cook for about 5-6 minutes until crispy.
With a hand-held blender whip goat cheese and cream with the rest of the cheese spread ingredients to form a smooth spread.
Cook patties over medium high heat on the grill for about 4 minutes a side until nice grill marks appear.
To assemble, place lettuce on bottom bun, then place beet burger, whipped goat cheese, radishes and top with crispy quinoa.