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

Combine the ricotta cheese and granulated sugar in a large mixing bowl and beat on medium speed until smooth and creamy, about 2 minutes.

Incorporate eggs one at a time, mixing well after each addition until fully combined.

Stir in melted butter, lemon zest, lemon juice, and vanilla using a spatula, folding gently.

Whisk together flour, baking powder, and salt in a separate bowl, then gradually add to the wet mixture, stirring until just combined.

Fold in the chopped pistachios gently into the batter.

Pour the batter into the prepared pan, smoothing the top, and fill it about two-thirds full.

Bake for 30-35 minutes, until the top is golden brown and a toothpick inserted in the center comes out clean.

Let the cake cool in the pan for 10 minutes then transfer to a wire rack to cool completely. Dust with powdered sugar and sprinkle with extra pistachios before serving.