Peel core and slice apples crosswise into ½" pieces. Place apples in a microwave-safe bowl. Cover and microwave until apple slices are bendable and slightly translucent, approximately 3 minutes.
Remove and pour off liquid. Gently toss the apples with the lemon juice and set aside to cool.
While the apples cool, spray a 6" springform pan with baking spray. Cut a round of parchment paper to fit the bottom of the pan. Place the parchment paper in the pan and lightly spray it with baking spray. Preheat the oven to 325°F.
Whisk ½ cup flour, ½ cup sugar, baking powder, and salt in a small bowl.
Whisk oil, milk, egg white, and vanilla in a medium-sized bowl.
Add the flour mixture to the milk mixture and whisk until just combined.
Measure out ½ cup of batter and put it in a third bowl, and set aside. Add the egg yolk to the remaining batter in the medium bowl and whisk to combine.
Gently fold the cooled apples into the batter in the medium bowl.
Pour the batter with the apples into the prepared springform pan, poking apples down and leveling the top.
Whisk the remaining 2 tablespoons of flour into the reserved cake batter.
Pour this batter over the batter with apples in the pan. Push batter to the edges of the pan and level the top.
Sprinkle the remaining 2 teaspoons of granulated over the top of the batter. Place the springform pan on a baking sheet and put it into the 325°F oven. Bake for 50 minutes or until a wooden skewer inserted in the center of the cake comes out clean.
Remove the cake from the oven and allow it to cool in the springform pan for 2-3 hours.
Remove the sides of the springform pan and remove the cake. Gently peel the parchment paper off the bottom and place on sa erving plate. Garnish with powdered sugar if desired.