Preheat oven to 170°C fan-forced. Grease and line a 22cm round cake tin.
Beat eggs and sugar until pale and thick, 3 minutes.
In a slow stream, whisk in the olive oil until emulsified. Add milk, orange juice, zest and vanilla. Mix until combined.
Sift flour, baking powder and salt. Fold into wet ingredients just until combined.
Pour into tin. Bake 45-50 minutes until deeply golden and a skewer comes out clean.
Cool in tin 10 minutes, turn out onto a rack.
Optional glaze: whisk icing sugar with orange juice until pourable. Drizzle over cooled cake, let drip down sides. Serve with mascarpone or Greek yoghurt.