Preheat your oven to 350°F (175°C). In a medium bowl, mix together the graham cracker crumbs and crushed pistachios until evenly combined. Pour in the melted butter and stir until the crumbs are fully coated and resemble wet sand. Press this mixture firmly into the bottom of your prepared 9x9-inch pan to form an even crust layer. Bake for 8-10 minutes until it’s slightly golden and fragrant. Remove from the oven and let cool while you prepare the filling.
Using an electric mixer, beat the softened cream cheese and granulated sugar together on medium speed until smooth and creamy. Add in the heavy cream, sour cream, and vanilla extract, then mix until fully incorporated. One at a time, add the eggs, beating gently after each addition to keep the mixture light. Avoid overmixing as this can create cracks during baking.
If your shredded phyllo dough is not pre-rinsed, place it in a fine sieve and rinse with cold water to remove excess starch. Drain well and pat dry with paper towels. This step ensures the topping crisps up beautifully without becoming soggy.
Pour the cheesecake filling over the cooled crust and smooth the top with a spatula. Evenly sprinkle the shredded phyllo dough over the cheesecake layer, gently pressing it down to adhere. Bake in the preheated oven for 40-45 minutes or until the edges are set but the center still has a slight jiggle.
While the bars bake, combine sugar and water in a small saucepan over medium heat. Stir until the sugar dissolves completely and the mixture comes to a gentle boil. Reduce heat and simmer for 5 minutes to thicken slightly. Remove from heat and stir in the rose water. Let cool to room temperature.
Once the cheesecake bars come out of the oven, let them cool for 10 minutes in the pan. Then, pour the cooled rose water syrup evenly over the top, allowing it to soak in. Chill the bars in the refrigerator for at least 3 hours or overnight for best flavor and texture. Cut into squares and serve chilled or at room temperature.