Preheat your oven to 350°F (175°C) and prepare a 9-inch pan by greasing it with butter and lining the bottom with parchment paper.

Finely process about a cup of unshelled pistachios in a food processor until crumb-like.

In a mixing bowl, whisk together 1.5 cups of all-purpose flour, 1 teaspoon of baking powder, and a pinch of salt.

In a stand mixer, beat together 0.5 cups of softened unsalted butter, 0.5 cups of vegetable oil, and 1 cup of granulated sugar with lemon zest until light and fluffy, about 3-4 minutes.

Add in the eggs one at a time, then incorporate 0.5 cups of sour cream, 1 teaspoon of vanilla extract, and 0.5 teaspoon of almond extract.

Gradually mix in the dry flour mixture and 0.5 cups of buttermilk, alternating between the two until just combined. Fold in the pistachio crumbs.

In a separate bowl, beat 8 ounces of softened cream cheese until smooth. Mix in one egg and gradually add 2 cups of powdered sugar along with another teaspoon of vanilla until thick.

Pour the cake batter into the prepared pan, dollop the cream cheese mixture on top, and bake for 40-45 minutes until the edges are golden and the center is slightly jiggly.

Let cool in the pan for 10-15 minutes, then transfer to the refrigerator and chill for at least 2 hours before serving.