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Preheat the oven to 350 degrees. Lightly grease and flour a 9" square pan with the olive oil and flour. Shake out the excess flour, and set the pan aside.
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Place the flour, sugar, baking powder, baking soda, and salt in a large mixing bowl and whisk to combine. Crack the eggs into the bowl and stir to break the yolks, then add the orange juice, zest, and olive oil. Mix with a wooden spoon until well combined, 60 to 70 strokes, or mix with an electric mixer on medium speed until smooth and combined, 1 to 2 minutes.
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Turn the batter into the prepared pan, place the pan in the oven, and bake until the cake is well browned and the top springs back when lightly pressed with a finger, 38 to 42 minutes.
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Remove the pan from the oven. Let the cake rest on a wire rack for 20 minutes. Run a knife around the edges, gently pop it out of the pan, and let it rest on the rack until cool, 30 minutes more.
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To serve, dust with powdered sugar; or for a sweeter cake, drizzle with Orange Glaze: Combine 1/4 cup orange juice with 1 1/4 cups powdered sugar, whisk until the mixture is smooth. Drizzle over the cake or over individual servings as desired.