Preheat the oven to 350°F (175°C). Grease an 8-inch (20 cm) round cake pan and line the bottom with parchment if desired.
In a bowl, mix the ground almonds, baking powder, and a pinch of salt.
In another bowl, whisk the eggs and sugar until pale and slightly foamy.
Whisk in the vanilla extract and orange zest, then whisk in the melted butter.
Add the almond mixture to the wet ingredients and stir until smooth.
Pour the batter into the prepared pan and level the top.
Bake until golden and a toothpick inserted in the center comes out clean.
Cool, dust with powdered sugar if using, slice, and serve.