In a medium bowl, combine the flour, cardamom, baking powder and salt with a whisk. Set aside.
In a food processor fitted with the knife blade, finely grind the pistachios. Change the blade to the dough blade. Add butter and sugar and beat in processor until light and creamy. mix in eggs, one at a time, stopping to scrape down sides. Add the remaining orange juice and zest, vanilla and the yogurt. Mix well. Add the four mixture and pulse just to combine, again scraping the bowl to make sure the batter is uniform. Briefly mix in any reserved rhubarb chunks.
Transfer batter to pan, on top of rhubarb stalks, and smooth top of batter.
Bake in oven for 1 hr. and 15min. The top should be browned and the edges bubbly. A cake tester inserted in the center will be clean.
Cool the cake for 5 minutes then run a small sharp knife around edges. Place a plate on top of the cake pan and invert. Slowly lift the cake pan away.
I prefer the cake warm with lightly sweetened and freshly made whipped cream or vanilla ice cream, but it can also be served at room temperature, as is.