Preheat oven to 350°F. Butter a 9-inch springform pan and sprinkle bottom and sides with powdered sugar. Set aside.
In a bowl, whisk together flour, granulated sugar, baking powder, and salt.
In another bowl, mix together ricotta, eggs, and vanilla until smooth. Stir in lemon zest and juice.
Add flour mixture to wet ingredients and stir until no dry streaks remain. Batter will be somewhat lumpy. Stir in melted butter, then fold in raspberries. Take care to not crush them, and save a few for scattering on top, if you like.
Spread batter into prepared pan and add extra raspberries on top if preferred. Bake for about 50 minutes, until a toothpick inserted in the center comes out clean.
Let cool in pan for 15 minutes, then open side and remove cake to a wire rack to cool completely or serve warm. Sprinkle powdered sugar over the top just before serving.