Preheat the oven to 355 degrees F/180 degrees C. Using a pastry brush and softened butter, brush an 8-inch/20 cm round cake pan or charlotte mold. Sift flour, baking powder, and salt using a flour sifter in a bowl. In a microwave-safe bowl, melt butter and let it cool.

To make the batter, in a large mixing bowl, whisk eggs and brown sugar at high speed with an electric or stand mixer fitted with the whisk attachment for about 5 minutes. Add warm melted butter, oil, lemon zest, and lemon juice to the egg mixture and combine. Add dry ingredients and gently smooth the mixture with a rubber spatula.

Pour the batter into the prepared cake pan and bake in the hot oven for 30 minutes. Check the cake's doneness with a toothpick or a sharp knife: the cake is ready if they come out clean. Let the cake cool for a few minutes, remove it from the mold, and cool down on a wire rack for 15 minutes. Dust the cake with confectioners' sugar if desired.