Preheat oven to 375°F (190°C). Line a 9x9 inch baking pan with parchment paper, leaving an overhang on two sides for easy removal.

Prepare the Crust/Crumble: In a large bowl, whisk together the flour, 3/4 cup sugar, baking powder, and salt. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs. Reserve 1 cup of this mixture for the topping.

Mix the remaining crumb mixture with 1 large egg until a soft dough forms. Press this dough evenly into the bottom of the prepared baking pan to form the crust. Bake the crust for 12 minutes until lightly golden.

While the crust bakes, prepare the fillings. For the Rhubarb Filling, toss the chopped rhubarb with 1/2 cup sugar and 2 tablespoons of flour. For the Cream Cheese Layer, beat the softened cream cheese, 1/4 cup sugar, 1 large egg, and vanilla extract until smooth and creamy.

Pour the cream cheese mixture evenly over the partially baked crust. Gently spoon the rhubarb mixture over the cream cheese layer. Sprinkle the reserved 1 cup of crumb topping evenly over the rhubarb.

Return the pan to the oven and bake for 35-40 minutes, or until the topping is golden brown and the cream cheese layer is set (it should not jiggle much in the center).

Let the bars cool completely in the pan on a wire rack (this is crucial for clean slicing). Once completely cool, use the parchment overhang to lift the slab and cut into 16 squares.