Preheat the oven to 350°F (175°C) and prepare your baking pan.
In a large mixing bowl, combine ricotta cheese and sugar.
Add the eggs one at a time, mixing well after each addition.
Stir in the melted butter and vanilla extract.
In a separate bowl, whisk together flour, cocoa powder, baking powder, and salt.
Gradually fold the dry ingredients into the ricotta mixture.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer it to a wire rack.
Serve the cake at room temperature, optionally dusting with powdered sugar.