Bring 2 cups water and ½ teaspoon salt to a boil, and add quinoa. Reduce heat and simmer 15 minutes or until quinoa is tender and water is absorbed. Remove from heat, and let cool to room temperature.
Combine cooked quinoa, garlic, cheese, and eggs in a medium bowl.
Stir in bread crumbs, and let sit a few minutes so crumbs can absorb some of the moisture. Add more bread crumbs if necessary, but mixture should be fairly moist.
Season with basil, salt and pepper.
Heat a nonstick skillet on high heat.
While pan is heating, form mixture into patties (this will make approximately 20 2-inch patties)
Add patties to the skillet so they fit with some room in between them. Cook for 5-7 minutes, or until the bottoms are deeply browned. Carefully flip the patties with a spatula, and cook the other side for another 5-7 minutes, or until golden.
Remove from the skillet, and cool on a wire rack while you cook the remaining patties.