Follow these steps to create the Mushroom Cheesecake with Feta and Parmesan Crust:

1. Preheat your oven to 350°F (175°C).
2. In a medium bowl, combine the crushed crackers and melted butter. Mix until well combined.
3. Press the cracker mixture into the bottom of a 9-inch springform pan, creating an even layer to form the crust.
4. In a skillet, heat the olive oil over medium heat. Add the chopped mushrooms and sauté until softened, about 5-7 minutes.
5. Stir in garlic powder, onion powder, thyme, salt, and pepper. Cook for an additional 2 minutes. Remove from heat and allow to cool slightly.
6. In a large mixing bowl, beat the softened cream cheese until smooth. Add the sour cream and lemon juice, mixing until well combined.
7. Incorporate the feta cheese and grated Parmesan cheese into the mixture, stirring until combined.
8. Add the sautéed mushrooms to the cheese mixture, folding them in gently.
9. Beat in the eggs, one at a time, until everything is fully incorporated.
10. Pour the cheese and mushroom mixture into the prepared crust, smoothing the top with a spatula.
11. Bake in the preheated oven for 45-50 minutes, or until the center is set and the top is lightly golden.
12. Once baked, turn off the oven and crack the door, allowing the cheesecake to cool gradually for about 30 minutes.
13. Carefully remove the cheesecake from the oven and let it cool at room temperature for an additional 30 minutes.
14. Once cooled, refrigerate the cheesecake for at least one hour before serving.