Preheat your oven to 300°F. Line a rimmed baking sheet with unbleached parchment paper and set it aside.
In the bowl of a food processor fitted with the steel blade, place the chopped shallot and garlic and pulse until finely minced. Add the garbanzo beans, the salt and the lemon juice, and pulse until mostly smooth. Add the eggs and pulse to combine. The mixture will have become relatively thin.
Add the bread crumbs and rolled oats, and pulse until the mixture begins to come together.
Transfer the mixture to a large bowl, add the quinoa and shredded carrots, and mix to combine well. Cover the bowl and place in the refrigerator until the mixture thickens and becomes firmer (about 15 minutes or up to overnight).
Remove the bowl from the refrigerator, uncover it, and, divide the mixture into 10 separate burger patties.
Moisten hands with cool water as often as necessary to prevent the mixture from sticking to your hands. Place each shaped patty on a paper towel and blot it dry.
Heat 2 tablespoons of ghee in a large, heavy-bottom saute pan over medium heat until the ghee is melted and begins to shimmer.
Place as many patties in the pan as will fit without touching one another and fry until golden brown on the underside (about 3 minutes).
Flip the patties and fry until golden brown on the other side (another 2 to 3 minutes). Remove the patties to the prepared baking sheet.
Repeat with the remaining patties, using the remaining ghee as necessary.
Place the baking sheet with the burgers on it in the preheated oven and bake for about 10 minutes, or until mostly firm to the touch. Serve warm.
Notes
How to avoid using a food processor.
If you either do not have or do not want to use a food processor, you can make these quinoa burgers entirely by hand. Simply mince the shallot, garlic and the garbanzo beans by hand as finely as possible, and press them into a paste with the flat of a chef’s knife. Proceed with the rest of the recipe by mixing the remaining ingredients together by hand.