Preheat the oven to 400 degrees. Place the beets on a piece of foil. Drizzle with 1 teaspoon olive oil, sprinkle with salt and pepper, then close up the foil to enclose the beets. Roast for about 60-90 minutes, or until they can be easily pierced with a knife. Set aside and allow to cool, then remove the skins and roughly chop.
Bring the lentils and 1 ½ cups of water up to a boil, cover, then reduce to a simmer. Cook over low heat until the lentils are tender, about 30 minutes. Drain any remaining water, then set aside to cool.
Add the remaining 1 teaspoon olive oil to a medium saucepan over medium heat. Add the onions, mushrooms and rosemary leaves and cook, stirring occasionally, until they're softened and lightly browned, about 10 minutes. Set aside to cool.
Add the oats to a food processor and process on high until they become a fine powder, about 30 seconds to one minute. Add the cashews and process until they're also a fine powder, another 30 seconds to one minute. Add the beets, mushrooms onions, salt and pepper, then pulse to combine, stopping to scrape down the sides as needed. When the vegetables are fully incorporated, add the lentils and pulse until a homogeneous mixture is formed. Taste for seasoning and add more salt if needed. Transfer to a bowl and refrigerate for about 1 hour. This step can be skipped, but a chilled mixture will be easier to form into patties.
Heat several tablespoons of olive oil in a large saute pan over medium high heat. Divide the mixture into 6 portions. Dampen your hands with water (this will help prevent the mixture from sticking) and gently form a loose patty. Place it in the pan and repeat with 2 more (adjust the amount to fit your pan as needed). Use your spatula to gently press down on each patty to flatten it and shape it into a burger. Cook until browned and crisp, then carefully flip and cook until browned and crisp on the other side. Transfer to paper towels to drain, then repeat with the remaining patties.
Serve with a green salad and green goddess dressing or hot sauce, if desired.