Preheat oven to 350°F. Brush a 9-inch spring form pan with ½ tbsp oil. Line the bottom of pan with parchment paper and brush paper with another ½ tbsp oil. Zest 1 orange.
Carefully separate the egg yolks and egg whites, placing whites and yolks in 2 separate large bowls. Add the salt to egg whites. Using a hand or stand mixer on medium speed, beat egg whites until stiff peaks form, about 2 min. Set aside.
Add the sugar to yolks and beat until smooth and fluffy, about 3 min. To the bowl, add remaining 6 tbsp oil, almond extract, vanilla extract, and orange zest and beat until combined. Using a spatula, stir in the almond flour until well mixed. Gently fold egg whites into cake batter, being careful not to deflate whites.
Transfer batter to prepared pan. Smooth top and sprinkle with the almonds. Bake 30–35 min., until a toothpick inserted into center comes out clean. Cool cake completely in pan on wire rack.
Meanwhile, cut all peel and pith from both oranges. Cut segments from oranges into a medium bowl and squeeze any juice from pulp. Run edge of butter knife or mini offset spatula around edges of cake to loosen. Remove ring from spring form pan. Spoon oranges over cake.