Preheat oven to 350°F. Line a 9x13-inch metal baking pan with parchment paper, leaving an overhang on two sides.
Make the crust: Beat butter and powdered sugar together until creamy. Add flour and salt and mix until the dough just comes together. Press evenly into the prepared pan.
Pre-bake the crust for 18–22 minutes until the edges are lightly golden. Remove from oven.
Make the custard: Whisk eggs, sugar, flour, cream, and vanilla together until smooth. Fold in the chopped rhubarb.
Pour the custard mixture over the pre-baked crust and spread evenly.
Bake for 40–45 minutes until the edges are set and the center has just a slight jiggle.
Cool completely at room temperature (about 1.5–2 hours), then refrigerate for at least 1 hour before cutting.
Lift bars out using the parchment overhang, slice into squares, and serve chilled.