Preheat oven to 350 degrees. In a large saucepan, bring 1 quart water to a boil over high heat. Add the walnuts and boil, uncovered, 1 minute. Drain well. Spread the walnuts on a cookie sheet lined with aluminium foil. Bake 15 to 20 minutes, or until golden and fragrant. Cool on a rack. Place the cooled walnuts in a food processor or blender with 1/2 cup cold water and process until almost a smooth paste, scraping down sides of the work bowl. Add 1/2 cup cold water and process until almost smooth. In a 2-quart saucepan, whisk the rice flour and 1 cup water until smooth. Whisk in the walnut puree and 2 1/2 cups cold water. Heat over medium-high heat, whisking constantly, until mixture comes to a boil. Cut the brown candy into smaller pieces. Add the brown candy, reduce to low and simmer 10 minutes, whisking occasionally. The soup should be the consistency of a light cream soup. If mixture is too thick, whisk in up to 1/2 cup more water. Serve piping hot.