Heat the oven to 350℉ and prepare your loaf pans by buttering and flouring them.
Chop the rhubarb into thin pieces about an eighth to a quarter inch thick. (And if using walnuts, chop them roughly.)
In a large bowl, whisk together the flour, baking soda, and salt.
In a medium bowl, whisk together the eggs, buttermilk, oil, and vanilla extract. Then add both sugars and stir until the mixture is well combined.
Add the wet mixture to the dry ingredients and stir until the batter is combined and no trace of flour remains.
Add the rhubarb (and walnuts, if using) and stir until evenly distributed through the batter.
Transfer the batter to the prepared pans.
Bake for about one hour if using 8x4 inch pans, and about 30 to 35 minutes for miniature loaves, or until a toothpick inserted into the center of each loaf comes out clean.
Cool on wire racks for about 10 minutes before turning the loaves out of their pans. Slice generously and serve.