Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch square cake pan.
Beat 2 tablespoons softened butter and 1 cup white sugar with an electric mixer in a large bowl until light and fluffy. Beat egg into the butter mixture.
Mix 2 cups flour, baking powder, baking soda, and salt in a bowl; add flour mixture alternately with buttermilk, to the butter mixture, stirring just to combine into a batter. Fold rhubarb into the batter just until incorporated; pour into prepared pan.
Stir 2 tablespoons melted butter, 1/4 cup flour, and 1/4 cup white sugar together in a bowl until evenly moist; sprinkle over the batter.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 35 to 40 minutes. Cool in the pan for 10 minutes before removing to cool completely on a wire rack.
Stir 1/2 cup butter, brown sugar, cream, and vanilla together in a saucepan over medium heat; bring to a boil and cook for 1 minute. Serve sauce immediately with the warm cake.