Prepare the ingredients. Cook the quinoa and roughly chop the vegetables.

Place the carrots, onions, and garlic into a food processor and process them into crumbles.

Remove the vegetables from the food processor and place them into a mixing bowl; add the mushroom pieces and walnuts and process.

Heat 1 tablespoon of olive oil in a skillet over medium heat and add all of the crumbled vegetables; cook them until they become soft - about 5 to 8 minutes.

Place the cooked veggies into a strainer and press down on them with a spoon over the sink to squeeze out as much liquid as you can from the mixture.

Add the strained veggies back to the mixing bowl and add the tamari sauce, egg and shredded cheese; mix well.

Place the mixture in the refrigerator for 45 minutes.

Form the chilled mixture into patties using your hands or a burger press.

Heat the remaining oil in a skillet and cook the burgers for 5 to 8 minutes, flip and cook for 5 minutes longer.