In a large bowl, combine quinoa, pumpkin, 3/4 cup basil, beet, oats, 1/4 cup goat cheese, garlic, salt, and ginger. Mix until well combined. Cover and chill for 30 minutes or until easy to work with.
In a very large skillet, heat oil over medium heat. Meanwhile, divide the mixture into 4 portions and press each portion into a 4-inch patty.
Cook patties in hot oil over medium heat for 12 to 15 minutes or until firm and lightly browned, turning once halfway through cooking.
Spread remaining 1/4 cup goat cheese over toasted bread slices. Top with quinoa burgers. If desired, garnish with additional fresh basil, diced tomato, and/or sliced red onion.
