Preheat oven to 325F. Grease a 9" springform pan and line the bottom with parchment paper.
In a large mixing bowl, whisk together the olive oil, sugar, orange zest, orange juice, and egg yolks.
1/2 cup extra-virgin olive oil, 1/4 cup granulated sugar, 1 Tbsp orange zest, 1/4 cup orange juice, 4 large egg yolks
In a small mixing bowl, toss together the almond flour, tapioca flour, baking powder, and salt. Add these to the wet ingredients and combine with a rubber spatula.
2 cups almond flour, 1/4 cup tapioca flour, 1 tsp baking powder, 1/4 tsp salt
In a medium mixing bowl, beat the egg whites with the cream of tartar until foamy. Continue beating while gradually adding the remaining sugar until stiff peaks form.
4 large egg whites, 1/2 tsp cream of tartar, 1/4 cup granulated sugar
Gently fold the egg whites into the batter in three equal parts until no streaks remain. Pour the batter into the prepared pan.
Bake for 35-40 minutes or until the center springs back when lightly pressed.
Notes
Store the cake covered at room temperature for up to 2 days, or refrigerate for up to 5 days. Bring to room temperature before serving.