Lentil Walnut Burgers

Name: Lentil Walnut Burgers
Ingredients: 1/4 cup finely chopped walnuts; 2 cups cooked brown rice, divided ( Learn to Cook: Brown Rice ); 1 small carrot, finely chopped; 2 teaspoons extra virgin olive oil; 1/2 teaspoon ground black pepper; 1/8 teaspoon cayenne (optional); 1 egg, lightly beaten; 1/2 cup chopped button mushrooms; 1 1/2 cups cooked lentils, or 1 (15-ounce) can lentils, rinsed and drained; 1 tablespoon finely chopped parsley; 1/4 cup chopped celery; 1/2 teaspoon sea salt; 1 teaspoon chopped fresh thyme; 2 tablespoons high heat sunflower oil or expeller-pressed canola oil, divided