Preheat your oven to 350°F (175°C). Grease a baking pan.
In a mixing bowl, combine flour, sugar, baking powder, salt, and cold butter. Mix until crumbly, then press into the bottom of the prepared pan.
In another bowl, mix the chopped rhubarb, granulated sugar, cornstarch, lemon zest, and vanilla extract. Spread this mixture over the crust.
In a separate bowl, beat cream cheese with sugar until smooth. Add the egg and vanilla extract, mixing until well combined. Pour over the rhubarb layer.
Bake for 40 minutes or until set. Let it cool before cutting into squares.
Notes
For a sweeter dessert, increase the sugar in the rhubarb filling. Serve chilled for best flavor.