Prepare the Crust:
Preheat the oven to 325°F (163°C).
In a small bowl, combine the graham cracker crumbs, melted butter, and chopped pistachios (if using). Stir until the mixture is evenly coated and the crumbs are slightly damp.
Press the mixture into the bottom of a springform pan to form an even crust. Bake for 10-12 minutes, until slightly golden. Remove from the oven and set aside to cool.

Sauté the Mushrooms:
In a pan, heat the olive oil over medium heat. Add the chopped mushrooms and cook until they are softened and any excess moisture has evaporated, about 5-7 minutes. Stir in the garlic powder, onion powder, salt, and pepper. Set aside to cool slightly.

Make the Filling:
In a large mixing bowl, beat the cream cheese until smooth and creamy.
Add the sour cream and heavy cream, continuing to mix until fully combined.
Stir in the sautéed mushrooms, finely chopped pistachios, and fresh thyme (if using).
Beat in the eggs, one at a time, until just combined. Be careful not to overmix. Taste and adjust seasoning with salt and pepper as needed.

Assemble the Cheesecake:
Pour the filling mixture over the cooled crust in the springform pan. Smooth the top with a spatula.

Bake:
Bake the cheesecake in the preheated oven for 50-60 minutes, or until the edges are set and the center is slightly jiggly. You can test doneness by gently shaking the pan—the center should be firm but have a slight wobble.
Turn off the oven and leave the cheesecake in the oven for 1 hour with the door slightly ajar to prevent cracking.

Cool and Chill:
Let the cheesecake cool at room temperature for about 30 minutes before transferring it to the refrigerator. Chill for at least 4 hours or overnight.

Serve:
Before serving, remove the cheesecake from the springform pan and garnish with chopped pistachios, fresh thyme sprigs, and extra sautéed mushrooms if desired.