Preheat oven to 350°F. Grease a 9-inch springform pan.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon.
In a large bowl, whisk together vegetable oil, white sugar, brown sugar, and eggs until well combined.
Gradually whisk in the flour mixture until just combined. Stir in grated carrots.
Pour the batter into the prepared pan and bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean. Let cool completely.
In a large bowl, using an electric mixer, beat together the cream cheese, olive oil, and white sugar. Add eggs, one at a time, beating well after each addition. Stir in lemon juice.
Pour the cheesecake mixture over the cooled carrot cake base and bake for 20-25 minutes, or until set. Let cool completely.
In a medium bowl, whisk together peanut butter, powdered sugar, and heavy cream until smooth.
Spoon the peanut butter mixture over the cooled cheesecake and sprinkle with chopped peanut butter cups. Serve immediately or refrigerate until ready to serve.