Preheat oven to 325°F. Prepare a 9" springform pan with a parchment liner and cake slip.
In the first bowl, whisk together the flour, baking powder, baking soda, and salt. Set the dry ingredients aside.
In a second bowl, combine the milk and Grand Marnier. In a separate measuring cup, measure out 1 cup of EVOO. Set the wet ingredients aside.
Put the eggs and sugar in a large bowl or stand mixer and whisk until well-combined and smooth.
Gradually add the olive oil in a steady stream while whisking the egg mixture, as if you were making a mayonnaise.
After you have emulsified the oil into the egg mixture, start adding the dry ingredients in 3 additions, alternating with the wet ingredients in 2 additions, beginning and ending with dry. As you make each addition of dry and wet ingredients, whisk until the batter is smooth, without overbeating.
Pour the batter into the prepared pan. Bake the cake until deep golden brown, slightly domed, and possibly cracked on top, about 70-90 minutes. A skewer should come out clean of batter but with a few moist crumbs.
Let the cake cool. Level off the top of the cake with a serrated knife. Spread labneh evenly on top and sprinkle with figs.