Place oranges in a small to medium saucepan, then fill with enough water to cover (although they will float). Place over medium-high heat until boiling. Turn down heat to reduce to a simmer, and cook for 30 minutes. Drain and let cool slightly, then place in a blender or food processor and pulse until a paste is formed.
While oranges are boiling, place almond flour in a large skillet over medium heat. Cook until flour begins to brown lightly and smells very fragrant. Remove from heat and let cool.
Preheat oven to 350 degrees F. Grease a 9 or 10 inch round springform pan.
In a small bowl, whisk together toasted almond flour, all purpose flour, salt, and baking powder. Set aside.
In a mixing bowl, beat together eggs and sugar until light and airy, about 1-2 minutes. Add olive oil and paste made from oranges and mix until just combined. Add flour mixture and mix until just barely combined.
Pour batter into prepared pan and cook in preheated oven for 45-55 minutes, until a toothpick inserted in the center comes out clean.