In a large bowl, combine the flour, brown sugar, baking soda and salt. In a small bowl, beat the eggs, buttermilk, oil and vanilla. Stir into dry ingredients just until moistened. Fold in rhubarb and walnuts.
Fill greased or paper-lined muffin cups three-fourths full. Bake at 375° for 18-20 minutes or until a toothpick comes out clean. Cool for 5 minutes before removing from pans to wire racks. Serve warm.