Prepare the pistachio filling.
In a food processor, pulse the pistachios, 1 tablespoon ghee, and 2 tablespoons sugar until roughly chopped and evenly combined. Avoid processing into a paste.
Alternatively, finely chop the pistachios by hand and stir together with the ghee and sugar.
Reserve 1/4 cup of the mixture for the topping.
Prepare the pan and oven.
Preheat the oven to 350°F. Brush the bottom and sides of a 9-inch springform pan with melted ghee.
Place the pan on a rimmed baking sheet to catch any drips.
Build the phyllo base.
Brush 4 phyllo sheets individually with melted ghee and layer them in the pan, turning each slightly so they cover the bottom and come up the sides.
Spread the pistachio mixture over the base, keeping the reserved 1/4 cup aside.
Keep unused phyllo covered while you work so it doesn’t dry out.
Make the cheesecake filling.
Beat the softened cream cheese until smooth. Add the sugar and mix until fully combined, scraping down the bowl as needed.
Add the eggs one at a time, mixing on low just until each is incorporated. Add the vanilla and mix briefly until smooth. Avoid whipping excess air into the filling.
Assemble.
Pour the cheesecake filling over the pistachio layer and gently smooth the surface.
Sprinkle the reserved pistachio mixture over the filling.
Brush 3 more phyllo sheets individually with melted ghee. Loosely arrange them over the cheesecake, gently ruffling or folding them to fit inside the pan without pressing them into the batter.
Bake.
Bake for 55–60 minutes, until the edges of the cheesecake are set and the center still has a gentle wobble. The center should not look liquid. Add a little baking time if needed.
Check the phyllo during baking. If it browns too quickly, loosely tent the top with foil.
Cool gradually.
Turn off the oven and leave the cheesecake inside with the door slightly open for about 1 hour.
Remove and let cool further on a wire rack. Refrigerate within 2 hours of removing it from the oven, then chill for at least 6 hours, preferably overnight. Cover once cold.
Finish and serve.
Carefully release the cheesecake from the springform pan.
Drizzle lightly with cooled simple syrup or honey syrup just before serving. Slice with a sharp knife and offer extra syrup on the side.