Step 1: Preheat your oven to 350°F (175°C). Pour the 1/4 cup of melted butter into a 9-inch round cake pan and swirl to coat the bottom. Sprinkle the 1/2 cup of sugar evenly over the butter.
Step 2: Arrange the rhubarb pieces over the sugar in a decorative pattern, packing them tightly as they will shrink slightly during baking.
Step 3: In a large bowl, cream together the 1/2 cup of room-temperature butter and 3/4 cup of sugar until light and fluffy.
Step 4: Beat in the egg and vanilla extract until well combined.
Step 5: In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Step 6: Gradually add the dry ingredients to the butter mixture, alternating with the sour cream, beginning and ending with the dry ingredients. Mix until just combined.
Step 7: Gently spread the batter over the rhubarb in the pan, being careful not to disturb the fruit arrangement.
Step 8: Bake for 40-45 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Step 9: Let the cake cool in the pan for 10 minutes. Run a knife around the edge, then carefully invert the cake onto a serving plate or wire rack.