Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9-inch round cake pan.
Whisk ricotta cheese and sugar together in a large bowl. Whisk in eggs one at a time until well combined.
Combine flour and baking powder in a bowl; sift into ricotta mixture. Mix until batter is well combined and no dry spots remain. Add chopped chocolate, melted butter, and vanilla extract; stir until batter is smooth. Pour into the prepared cake pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Cool completely in the pan before serving.