Preheat oven to 325 degrees. Spray a glass 9x13x2-inch pan.
In a large mixing bowl, sift together flour, baking soda, and salt. Stir in brown sugar and set aside. In another bowl, mix buttermilk, egg, vegetable oil, and vanilla extract. Add rhubarb and walnuts, stirring until blended. Add wet ingredients to dry ingredients and stir, just until combined. Spread into prepared pan and bake 55 minutes.