Combine quinoa with 1 ⅓ cups water and bring to a boil. Reduce heat to a simmer, cover, and cook for 20 minutes or until all water is absorbed. Be sure quinoa isn't boiling, but cooking at a gentle simmer. Remove from heat, uncover and let cool for at least 10 minutes. Fluff quinoa with a fork.
Combine quinoa, eggs, sea salt and pepper in a medium bowl. Stir in thyme, garlic and cheese, if using. Add bread crumbs and stir until just combined. If mixture seems overly wet, add a tablespoon or two more of bread crumbs. If it seems too dry, add a tablespoon or two of water or broth. Let stand for about five minutes so liquid can be absorbed. Take small handfuls of mixture and form little patties, about 1-inch thick.
In a large skillet, heat olive oil over medium heat. Add a single layer of patties and cook until bottoms are well-browned, about 5-7 minutes, adjusting heat as necessary to prevent burning. Flip patties and cook about 5 minutes until second side is golden brown. Remove from skillet and repeat with remaining patties (adding a bit more olive oil, if needed). Serve over salad or with a creamy dipping sauce.