Preheat the oven to 350°F.
In a mixing bowl, combine crushed graham crackers, melted butter, feta cheese, and Parmesan cheese. Mix until well combined.
Press the mixture firmly into the bottom of a 9-inch springform pan to form the crust.
In a skillet, heat olive oil over medium heat. Add chopped mushrooms and sauté until they are soft and any moisture has evaporated, about 5-7 minutes. Season with salt and pepper. Remove from heat and let cool slightly.
In a large mixing bowl, beat the softened cream cheese until smooth. Add sour cream, heavy cream, garlic powder, onion powder, and eggs. Mix until well combined and creamy.
Fold in the sautéed mushrooms and chopped pistachios.
Pour the cream cheese mixture over the prepared crust in the springform pan. Smooth the top with a spatula.
Bake in the preheated oven for 50-60 minutes, or until the center is set and slightly jiggles.
Turn off the oven and leave the cheesecake inside for 1 hour to cool gradually.
Remove the cheesecake from the oven and let it cool to room temperature. Once cooled, refrigerate for at least 4 hours or overnight before serving.