Heat Oven: Heat the oven to 350° F.
Prepare Cake Pan: Line 9-inch cake pan with with parchment paper and spray exposed sides with baking spray. Arrange cut figs in a single layer over parchment paper in concentric circles, packing them pretty close together. It's okay if they slightly overlap, and if there are small gaps.
Combine Liquid Ingredients: In a large mixing bowl, whisk eggs, olive oil, sugar, almond milk, and vanilla.
Add Walnuts: Fold in walnut flour.
Add Dry Ingredients: In a sieve or sifter directly over bowl with liquid ingredients, sift flour, baking powder, and salt. Stir into liquid ingredients until just combined.
Bake Olive Oil Cake: Pour the Olive Oil Cake batter over figs in prepared pan and bake for 50 minutes, checking at 45 minutes with a cake tester. Cake is done when top is medium golden brown and tester comes out clean.
Cool Cake and Serve: Allow cake to cool in pan for 20 minutes. Remove from pan and let cake cook completely for an additional hour.