Start by preheating your oven to 350°F (175°C). Grease a 9-inch cake pan thoroughly and line the bottom with parchment paper. This step prevents sticking and makes removing the cake much easier after baking.
Add the pistachios to a food processor or blender and pulse until they resemble fine crumbs. The texture should be similar to sand so they mix evenly into the batter. This step helps distribute the pistachio flavor throughout the cake.
In a medium bowl, whisk together the flour, baking powder, and salt. Mixing the dry ingredients separately ensures that the baking powder spreads evenly through the batter. Set this bowl aside while preparing the wet ingredients.
In a mixing bowl, beat the softened butter, vegetable oil, sugar, and lemon zest until the mixture becomes light and fluffy. Creaming introduces air into the batter, which helps the cake become soft and tender.
Add the eggs and egg white one at a time, mixing after each addition. Then stir in the sour cream, vanilla extract, and almond extract. These ingredients provide moisture, flavor, and a smooth batter texture.
Gradually add the flour mixture while alternating with the buttermilk. Begin and end with the dry ingredients, mixing only until combined. Overmixing can make the cake dense, so keep the mixing gentle.
Carefully fold the ground pistachios into the batter until evenly distributed. Pour the batter into the prepared pan and spread it evenly with a spatula. This layer forms the base of the dessert.
In another bowl, beat the cream cheese until smooth. Add the egg and vanilla extract, then gradually mix in the powdered sugar one cup at a time. The mixture should become thick, creamy, and lump-free.
Pour the cream cheese mixture over the pistachio cake batter. Use a spatula to gently spread it into an even layer so the entire cake is covered.
Place the pan in the oven and bake for about 40–45 minutes. The edges should turn golden while the center remains slightly jiggly. This soft center is what creates the classic gooey texture.
Allow the cake to cool for about 10–15 minutes, then place it in the refrigerator for at least 2 hours. Chilling helps the cream cheese layer firm up and improves the overall texture.