Preheat the oven to 350°F (180°C).
In a large bowl, beat the eggs and sugar using an electric mixer until well combined.
Add the vanilla extract. In a separate bowl, whisk together the flour, baking powder, and salt. Gradually incorporate the dry ingredients into the egg mixture.
In a small saucepan, heat the milk and butter until the butter is fully melted and the mixture is hot.
Slowly pour the warm milk into the batter, whisking continuously until smooth.
Transfer the batter to a 9-inch round cake pan and bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
Mix the cinnamon and sugar together, then sprinkle the mixture over the top of the cake before serving.