Position a rack in the center of the oven and preheat to 350°F. Set a 9-inch cake pan on a sheet of parchment paper. Trace the bottom of the pan onto the paper, then cut out the circle. Lightly coat the pan with nonstick spray, making sure to coat the sides. Place the parchment round inside the pan and gently press it in place. Set aside.
In a large bowl using a handheld mixer (or stand mixer fitted with the whisk), beat the eggs on medium speed until pale yellow and frothy, 2 to 3 minutes. Add the Greek yogurt, olive oil, maple syrup, orange zest, lemon zest, orange juice, lemon juice, vanilla extract, and almond extract. Beat until well combined.
Place the pistachios in food processor and blend until just finely ground. (Don’t over blend or it starts to get pasty). Place in a separate large bowl with the almond flour, tapioca flour, salt, baking powder, and baking soda. Whisk to combine. It’s okay if there are still lumps, just whisk as well as you can.
In 1-cup increments, slowly add the flour mixture to the wet ingredients, and beat at medium speed until just smooth. Carefully pour the batter into the prepared pan. Tap the cake pan lightly on the counter to release any air bubbles.
Bake on the middle rack until the cake is golden brown and a toothpick or cake tester inserted into the center of the cake comes out clean, 40 to 45 minutes. If the cake begins to brown too quickly, place a sheet of foil loosely over the top.
Remove the cake from the oven and let it rest in the pan for 10 minutes. Run a butter knife around the edges to loosen it. Place a wire cooling rack on top of the cake pan and carefully flip it over so the cake releases onto the rack. Peel off the parchment paper. Using your hands or a sturdy spatula, gently flip the cake right-side up. Let it cool for 10 to 15 more minutes before slicing and serving.