Preheat Oven: Set your oven to 375°F. Line an 8×8-inch baking pan with parchment paper, allowing some overhang for easy removal.

Prepare Raspberry Filling: In a saucepan, combine water, lemon juice, sugar, and cornstarch. Cook over medium heat, stirring constantly, until the mixture thickens and becomes bubbly (about 2-3 minutes). Continue cooking for an additional 2 minutes. Remove from heat and gently fold in the raspberries. Set aside to cool.

Make Crust & Crumb Topping: In a large bowl, whisk together sugar, flour, lemon zest, baking powder, and salt. Using a pastry cutter or two knives, cut in the cold butter until the mixture resembles coarse crumbs. Add the egg and mix until combined; the dough will be crumbly. Reserve 1/2 cup of this mixture for the topping. Press the remaining dough evenly into the bottom of the prepared pan.

Prepare Cheesecake Layer: In a separate bowl, beat the softened cream cheese and sugar until smooth. Add the egg, vanilla extract, and lemon juice, mixing until well combined. Pour this mixture over the crust in the pan, spreading evenly.

Assemble Bars: Spoon the raspberry filling over the cheesecake layer, spreading gently. Sprinkle the reserved crumb mixture evenly over the top.

Bake: Place the pan in the preheated oven and bake for 38-40 minutes, or until the top is golden brown and the center is set with a slight jiggle.

Cool & Serve: Allow the bars to cool completely in the pan. Once cooled, refrigerate for at least 1 hour before lifting out of the pan and cutting into 12 bars.