Boil the quinoa, and then drain it and remove from the heat. Add the cheddar and chives, and season to taste. Add the egg, and mix until fully incorporated.
Line a baking sheet with baking paper, and form the quinoa mixture into around three or four round patties. I used a baking ring to help me shape mine, but you can do them freeform too. Depending on how tall you make them, they may spread a little as they cook, so leave an inch or so in between them.
Bake for 30 minutes, or until firm and golden brown. Serve hot or cold, with a good dollop of homemade tartar sauce!