Preheat oven to 350°F. Grease and lightly flour a tube pan.
In a large bowl, whisk together the flour and baking powder.
In another bowl, beat the eggs with an electric mixer while slowly adding the sugar. Mix in the oil and vanilla until smooth.
Add the wet mixture to the dry ingredients using a wooden spoon, along with the orange juice. Stir until the batter is smooth
Thinly slice one apple. Pour half the batter into the pan and arrange the apple slices on top in a diagonal pattern. Sprinkle with half the sugar–cinnamon mixture.
Slice the second apple and toss the slices with the remaining sugar mixture. Pour the rest of the batter into the pan and top with the coated apples, pressing them gently into the batter.
Bake on the middle rack for 55–60 minutes, adjusting for your oven. (I moved it down one rack for the last 15 minutes and baked for 55 minutes total.)
Cool in the pan for 15 minutes, then invert onto a plate. Dust with powdered sugar before serving.