Preheat the oven to 350°F (175°C) and place the oven rack in the middle position.

Butter the sides and bottom of a 9-inch springform pan and set the pan aside.

In a medium bowl, whisk together 2 1/2 cups all-purpose flour, 2 1/2 teaspoons baking powder, 1/2 teaspoon baking soda, and 1/4 teaspoon salt.

In a large bowl, whisk 1 1/2 cups sugar with 1 3/4 cups sour cream (or plain yogurt), 3 large room-temperature eggs, 1/2 cup extra virgin olive oil, 2 tablespoons orange juice, 1 tablespoon orange zest, and 1 teaspoon orange extract until fully combined and creamy.

Add half of the dry ingredients to the wet ingredients and stir until just combined. Add the remaining dry ingredients and mix until the batter is smooth and no lumps remain; avoid overmixing.

Pour the batter into the prepared springform pan and smooth the top with a spatula.

Bake on the middle rack for 50–60 minutes, or until a toothpick inserted into the center comes out clean. If the top browns too quickly, tent the cake loosely with foil.

Remove the cake from the oven and place the pan on a cooling rack. Cool in the pan for 15 minutes.

Run a knife around the cake edge, release the springform, transfer the cake to the cooling rack, and cool completely before slicing and serving.