Pre-heat oven to 350° F. Grease or butter a 9″ cake pan and line the bottom with parchment paper.
Combine lemon zest and sugar in a bowl, rub zest into the sugar to release essential oils—set aside. Combine melted butter, olive oil and lemon juice in a medium bowl. In a separate bowl, together flour and baking powder.
In the bowl of a stand mixer fitted with the whisk attachment, combine eggs, sugar mixture and salt. Beat at high speed until vit basically doubles in size and is a super light yellow color. The mixture should be thick, real thick, so you want to mix this for like 10 minutes minimum on a medium-high speed. With mixer still running on high, SLOWLY add oil mixture to egg mixture. ANd when I say slowly I mean like a drizzle. If you do this properly the mixture will not separate, instead it will emulsify and look lovely, almost like a thin mayonnaise (it sounds gross, but trust me it is what you want).
Remove the bowl and fold in the flour mixture. Don't overmix or you'll have a tough cake.
Pour into the greased, lined pan and bake for 35-40 minutes or until the cake is set. A toothpick in the center will come out clean. Cool for 10 mins in the pan and then turn out onto a cooling rack and cool completely. Slice and serve with whipped mascarpone (beat mascarpone with a whisk or a stand or handheld mixer, drizzled with honey and a few pistachios...or use your favorite fruit compote.