Preheat oven to 350℉. Wrap the outside of a 9-inch springform pan with aluminum foil to prevent leaking, because it will leak. Sift together the 1 1/2 cups all-purpose flour, 1 1/2 teaspoons baking powder, 1 teaspoon baking soda, and 1/4 teaspoon salt. Set aside.
In a saucepan over medium heat, combine 2/3 cup brown sugar and 1/2 cup butter. Bring to a boil, then add 2 cups fresh rhubarb and 3/4 cup walnuts (if using), stir, and pour into bottom of springform pan. Do not overcook the sugar mixture.
In a large bowl, cream together the 1/2 cup butter and 3/4 cup white sugar until light and fluffy. Beat in the 2 eggs one at a time, then stir in the 1 teaspoon vanilla extract. Beat in the flour mixture alternately with the 1 cup sour cream. Pour batter into the prepared pan.
Bake in the preheated oven for 60 minutes, or until a toothpick inserted into the center of the cake comes out clean. The internal temperature of the cake should reach 200-210°F when it's fully baked. Using an instant-read thermometer inserted into the center of the cake (avoiding the bottom of the pan) is the most reliable way to check for doneness. Cool in the pan for 10 minutes, then invert onto serving platter and carefully release ring and remove pan. Serve warm with whipped cream, if desired.