Combine the quinoa, eggs, and salt in a medium bowl. Stir in the chives, onion, cheese, and garlic. Add the bread crumbs, stir, and let stand for a few minutes. Form mixture into twelve 1-inch thick patties. (Add more breadcrumbs if the mixture is too wet; add water if too dry.) Mixture can be kept covered in the refrigerator for up to 2 days.
Heat oil in a large, heavy skillet over medium-low heat. Working in batches, add patties, cover, and cook until bottoms are deeply browned, about 7 to 10 minutes. Increase heat to medium if there is no browning after 10 minutes and continue to cook until patties are browned. Flip patties with a spatula and cook the second sides until golden, about 7 minutes. Remove from skillet and cool on a wire rack. Repeat with remaining patties.