Preheat your oven to 350°F. Grease a 9-inch springform pan.
In a medium bowl, combine crushed feta cheese, grated Parmesan cheese, melted butter, flour, garlic powder, and salt. Mix until well combined.
Press the mixture firmly into the bottom of the prepared springform pan to form the crust. Bake for 10 minutes, then remove from the oven and let cool slightly.
In a large mixing bowl, beat together the cream cheese, ricotta cheese, and sour cream until smooth.
Add the eggs one at a time, mixing well after each addition.
Stir in the chopped mushrooms, pistachios, thyme, black pepper, and lemon juice until evenly distributed.
Pour the cheese mixture over the cooled crust in the springform pan. Smooth the top with a spatula.
Bake for 45-50 minutes, or until the edges are set and the center is slightly jiggly.
Turn off the oven and leave the cheesecake inside for an additional 30 minutes.
Remove the cheesecake from the oven and let it cool to room temperature. Once cooled, refrigerate for at least 4 hours, or overnight for best results.
To serve, carefully remove the sides of the springform pan. Slice and enjoy!