Set your oven to 400 degrees. Line a loaf pan (8.5 x 4.5) with parchment paper. If you don’t have parchment, oil the bottom and sides with ghee, or coconut oil.
Put 1 tablespoon cheese to the side. In a large bowl, mix together the rice, walnuts, all the rest of the cheese, celery and caraway seeds. Whisk the eggs together and stir into the rice mixture to completely cover. Add the tamari, ghee/oil, salt, and peppers, this time just lightly mixing to spread the seasonings through.
Spoon the mixture into the loaf pan. Use your clean hands, or a spatula, to press down and push it into the corners. Sprinkle the remaining cheese over the top.
Set the loaf pan in your oven, and cook for about 45 minutes or until a toothpick comes out clean.