Preheat the oven to 350°F (175°C). Grease a 9x9-inch baking pan.
In a mixing bowl, combine 1 cup of flour, 1/4 cup of sugar, 1/4 teaspoon of salt, and baking powder. Stir in the cold water until a dough forms.
Press the dough evenly into the bottom of the prepared baking pan to form the crust.
In another bowl, combine the chopped rhubarb, 1 cup of sugar, 1/4 cup of flour, salt, vanilla extract, and eggs. Mix until well combined.
Pour the rhubarb mixture over the crust in the baking pan, spreading it evenly.
Bake in the preheated oven for 35-40 minutes, or until the custard 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.