1. Preheat the oven to 375 degrees. Either steam the beet greens for 2 minutes above 1 inch boiling water, or blanch in salted boiling water for 1 minute. Transfer to a bowl of cold water, drain, squeeze out excess water, and chop medium-fine. Place in a large bowl with the cooked quinoa.
2. Heat 1 tablespoon of the oil over medium heat in a heavy skillet and add the onion and carrot. Cook, stirring often, until vegetables are just about tender, about 3 minutes, and add the ginger and a pinch of salt. Cook for another 3 minutes or so, until the vegetables are tender and fragrant, and add the cumin and the garlic. Cook, stirring, for another minute, and remove from the heat. Stir into the quinoa mixture.
3. In a food processor fitted with the steel blade, or in a bowl using a fork or a potato masher, purée the chickpeas with the lemon juice and, if using, the egg. Add to the quinoa mixture and stir everything together. Season to taste with salt and pepper.
4. Begin heating a heavy ovenproof skillet over medium-high heat. Seasoned cast iron is good, and so is a heavy nonstick pan that can go into the oven. Moisten your hands lightly and shape 4 large or 6 smaller patties. Add the remaining tablespoon of oil to the pan and, working in batches if necessary, cook the patties for 1 to 2 minutes on one side, until nicely browned. Carefully turn the patties over and place the pan in the oven. Bake 10 to 15 minutes, until the patties are lightly browned; if they fall apart you can patch them together with some pressure from the spatula. Remove from the heat and serve, with or without buns, ketchup and the works.
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