Preheat your oven to 350°F (175°C). Combine crushed shelled pistachios, grated parmesan cheese, melted butter, salt, and pepper in a food processor and pulse until well mixed and crumbly. Press this mixture into the bottom of a greased springform pan. Bake for 10-12 minutes, until slightly golden. Allow to cool.

In a skillet, add a drizzle of olive oil and warm it over medium heat. Add sliced mushrooms and sauté for about 5-7 minutes until golden brown. Season with salt and pepper and remove from heat to cool.

Beat softened cream cheese in a large mixing bowl until smooth. Gradually add the sour cream and mix until combined. Incorporate eggs one at a time, ensuring each is fully mixed before adding the next.

Gently fold in the cooled sautéed mushrooms and crumbled feta into the cream cheese mixture. Mix carefully with a spatula, ensuring even distribution of mushrooms.

Pour the filling over the prepared crust in the springform pan and smooth the top. Bake for 45-50 minutes, until edges are set but the center jiggles slightly.

Turn off the oven and crack the door slightly, allowing the cheesecake to cool gradually for 10-15 minutes. Then, cool to room temperature on a wire rack and refrigerate for at least four hours or overnight.