Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan with butter or non-stick spray, lining the bottom with parchment paper.

In a large mixing bowl, combine the ricotta cheese and granulated sugar, beating until smooth and fluffy for about 2-3 minutes.

Add large eggs one at a time, beating well after each addition for a well-emulsified batter.

Stir in melted unsalted butter, lemon zest, lemon juice, and vanilla extract, folding gently until just combined.

In a separate bowl, whisk together flour, baking powder, and salt, then gradually add to the ricotta mixture, folding until just combined.

Fold in chopped pistachios, ensuring they're evenly distributed within the batter.

Pour the batter into the prepared pan and bake for 30-35 minutes, or until golden brown and a toothpick comes out clean.

Allow the cake to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.

Dust the cooled cake with powdered sugar and garnish with chopped pistachios before serving.