Preheat the oven to 350ºF (180ºC) and line an 8 or 9-inch (20 or 23-cm) square baking dish with parchment paper.
In a mixing bowl, beat the butter and sugar together until light and fluffy, about 1 to 2 minutes.
Add the flour and salt, and continue to mix on low until the dough is crumbly with no visible flour remaining.
Dump the dough crumbs into the prepared baking dish. Use your hands to first spread, then press the crust evenly into the pan creating a tightly packed shortbread layer.
Place the crust into the preheated oven for 24 to 26 minutes or until the edges turn slightly golden. Remove the crust from the oven and place it on a wire cooling rack.
Make The Custard
While the crust is in the oven, make the custard. Using the same mixing bowl, combine the sugar, egg, and yolks. Mix everything together on low speed until smooth.
Add the flour and salt to the mixture and continue to mix on low until no visible streaks of flour remain, scraping the sides of the bowl down halfway through mixing.
Add the chopped rhubarb to the custard and fold it in gently until well coated.
Pour the rhubarb custard mixture over the pre-baked shortbread crust. Use a rubber spatula or fork to spread the rhubarb into an even layer.
Place the baking dish back in the oven and bake the rhubarb custard bars for 42 to 45 to minutes, or until the custard is set. Place the baking dish on a wire rack and cool the bars completely before slicing.