1. To make dressing: Combine the cilantro, lime juice, lime zest, and 1/4 teaspoon of the salt in a small bowl; whisk in 2 tablespoons of the oil in a slow, steady stream. Set aside.

2. Heat 1 tablespoon of the remaining oil in a medium nonstick skillet over medium heat. Add the mushrooms, onion, garlic, and cumin and cook, stirring occasionally, until softened, 4 to 5 minutes.

3. Add the walnuts and cook until the nuts are lightly toasted, 2 to 3 minutes.

4. Transfer to a bowl. Combine the lentils and rice in the bowl of a food processor and pulse until coarsely chopped; add to the mushrooms.

5. Stir in the parsley, remaining 1/4 teaspoon salt, and the pepper. Form into six 1/2-inch thick patties. Heat the remaining 2 tablespoons oil in a large nonstick skillet over medium heat.

6. Add the patties and cook, turning once, until browned and heated through 9 to 10 minutes (You can cook in 2 batches of 3 patties each if you don’t have a skillet large enough for all 6.)

7. Transfer to serving plates and top with any of the optional toppings and the cilantro dressing.