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Coat the bottom of a large skillet with olive oil and place it over medium-low heat. Add the onion and stir a few times to coat with the oil. Allow to cook for 45 minutes to 1 hour, stirring occasionally, until the onions are browned and caramelized. Stir in the garlic, raise heat to medium, and cook for another minute, until very fragrant. Remove from heat and transfer the onions to a plate.
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Place the oats into the bowl of a food processor and blend to a flour. Add in the lentils, walnuts, parsley, thyme, soy sauce, Worcestershire sauce, black pepper, and about ⅔ of the caramelized onions. Pulse until the ingredients are well mixed, being careful not to overdo it. Taste-test and adjust the seasonings to your liking.
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Make the cashew cheese by placing the cashews, garlic, red wine vinegar, milk, and salt into the bowl of a food processor and blending until smooth. Add in the herbs and pulse a few times until finely chopped and well mixed. Scoop the mixture into a bowl.
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To make the burgers, shape the lentil mixture into 4 to 6 patties. Add a touch more oil to the skillet you used for the onions and place it over medium heat. When the oil is hot, add the patties and cook for about 4 minutes on each side, until browned.
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Stuff the patties into buns or rolls and top with the cashew cheese, remaining caramelized onions, and any other toppings you like. Serve.