Add the mushrooms, oats, walnuts, garlic, egg, smoked paprika, black pepper, dried oregano, and sea salt to a food processor.
Pulse until the mixture is well combined but still slightly textured.
Let the mixture rest for 10 minutes so the oats absorb excess moisture.
Shape the mixture into 4-6 patties.
Heat the olive oil in a non-stick skillet over medium heat.
Pan-fry the patties until cooked through.