In a large skillet, heat a drizzle of olive oil over medium heat. Add the sliced mushrooms, grated carrot, and grated red onion. Season with salt and pepper. Sauté for about 5-7 minutes, or until the mushrooms are golden and any moisture has evaporated.
In a mixing bowl, mash the drained cannellini beans with a fork or a potato masher until mostly smooth but still chunky. If you're using a food processor, pulse the beans a few times, being careful not to over-blend.
To the mashed beans, add the sautéed vegetables, dry-roasted cashews (chopped roughly), panko breadcrumbs, grated Parmesan cheese, egg, mayonnaise, garlic powder, paprika, and cooked brown rice. Stir until everything is well combined.
Using your hands, form the mixture into patties, about 3-4 inches in diameter. If the mixture feels too wet, add a bit more panko breadcrumbs until it holds together.
Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper. Place the formed patties on the baking sheet and lightly brush the tops with olive oil. Bake for 25-30 minutes, flipping halfway through, until the patties are golden brown and firm.
Once baked, let the veggie burgers rest for a few minutes. Serve them on a bun with your favorite toppings and a drizzle of burger sauce if desired.
