Place the lentils in a small saucepan and cover with two inches of water. Add a pinch of salt and bring to a simmer over medium-high heat, then reduce the heat and simmer until the lentils are tender but still hold their shape, about 20 to 25 minutes. Drain thoroughly and set aside to cool.

Heat a portion of oil in a large skillet over medium-high heat until it shimmers. Add the mushrooms, onions, celery, leek, garlic, and a pinch of salt. Cook, stirring occasionally, until the vegetables are softened and any liquid released by the mushrooms has completely evaporated, about 10 minutes.

Process the cashews in a food processor until they are finely ground into a coarse meal, then transfer them to a large mixing bowl.

Pulse the cooked vegetable mixture in the food processor until coarsely chopped, then add it to the bowl with the cashews. Pulse the cooked lentils in the food processor separately until about half are broken down, then add them to the bowl.

Stir the bulgur, mayonnaise, panko, salt, and pepper into the mixture. The mix should be moist and hold together when pressed; let it rest for 10 minutes to allow the bulgur and panko to absorb the excess moisture from the vegetables.

Divide the mixture into 12 equal portions and shape them into patties about 1 inch thick.

Heat more oil in a large nonstick skillet over medium heat. Cook the patties in batches until they are deeply browned and have a crisp exterior, about 5 minutes per side, adding more oil as needed between batches.

Serve warm on buns with your favorite toppings.