Preheat the oven to 350 F. Start by prepping the rhubarb. Wash and dry the rhubarb and line it up next to an 8 inch round cake pan (you can also use a square pan). Start with your largest piece of rhubarb and cut it to fit in the center of the pan, then move outward.
Now grease the pan. Use butter or shortening to thoroughly grease the pan, on the bottom and up the sides. Add 1 tbsp of sugar to the bottom of the pan. Shake it around until it covers the entire bottom of the pan. Press the prepared rhubarb into the pan, lining the rhubarb up snugly side by side to each edge.
Add the butter and sugar to a large bowl. Mix for 2-3 minutes until totally combined and fluffy. Add eggs, grapefruit zest, and vanilla. Mix until just combined.
In a separate bowl, combine the dry ingredients -- flour, baking powder, and salt. Add half of the dry ingredients to the larger bowl. Mix until just under combined. Add half of the yogurt and mix until just combined. Repeat with the remaining dry ingredients and yogurt.
Transfer the batter to the prepared pan. Depending on how big your rhubarb is, you may have too much batter. If the batter is overflowing out of the pan, scoop it off until it is even with the height of the pan.
Bake for 45-55 minutes, until a toothpick comes out clean. Within the first 10 minutes of being out of the oven, carefully flip the pan over onto a cooling rack and slowly lift the pan up. You should be left with a beautiful upside down cake! Let it cool and enjoy.
Keep any extra cake in a sealable container.