Preheat oven to 350 degrees F.
Using either a food processor or a pastry blender and a large bowl, cut butter into 1 cup flour and powdered sugar mixture. If using a food processor, pulse 1 cup flour, powdered sugar and butter until you get a coarse powder mixture with pea sized bits of butter.
Press the mixture into a 7 1/2 x 11 inch pan or a 9 inch square pan. The mixture might feel dry like a powder, and that's ok.
Bake for 15 minutes in a preheated oven.
Meanwhile, in a large mixing bowl, combine eggs, white sugar, 1/4 cup flour, salt and rhubarb. (To easily chop rhubarb, pulse in the same food processor bowl that you used earlier.)
After 15 minutes, remove shortbread crust from the oven, and pour rhubarb mixture over top.
Return to the oven, and cook for an additional 35 minutes or until set and lightly golden brown.
Serve warm with a scoop of vanilla ice cream or whipped cream. Or let cool, and cut into rhubarb bars.