Preheat your oven to 350°F (175°C). Grease a 9x9-inch baking pan or line it with parchment paper for easy removal.
In a mixing bowl, combine 1 ½ cups flour, ½ cup sugar, softened butter, 1 teaspoon vanilla extract, and ¼ teaspoon salt. Mix until crumbly and well combined. Press the mixture evenly into the bottom of the prepared baking pan to form the crust.
In another bowl, combine the chopped rhubarb with 1 cup sugar, eggs, 1 teaspoon vanilla extract, ¼ cup flour, baking powder, and ¼ teaspoon salt. Whisk until smooth and well blended.
Pour the rhubarb custard filling over the crust in the baking pan. Bake for 35-40 minutes, or until the filling is set and the top is lightly golden.
Allow the bars to cool in the pan for at least 30 minutes before cutting into squares. For best results, chill in the refrigerator for an hour before serving.