Soak walnuts in hot water for 15–20 minutes. Drain and rinse well.
Add walnuts, mushrooms, onion to a food processor.
Pulse until combined and crumbly.
Transfer mixture to a hot pan, add salt, pepper, smoked paprika, garlic powder, onion powder, and mustard powder, then cook for about 7 minutes until browned and fragrant. Set aside to cool slightly.
In a small bowl, combine vegan mayo, ketchup, mustard, pickle or relish, hot sauce, dill, and lemon juice. Mix until smooth.
Peel potatoes and cut into thin strips. Toss with a little oil and salt, then roast at 400°F for 30 minutes or fry until crisp and golden.
Warm tortillas if desired. Layer with walnut meat, potato strings, burger sauce, lettuce, tomato, pickles, and plant-based cheese if using. Roll into burritos and serve.
