Prepare the Raspberry Jam Swirl:

Heat the oven to 350°F. Line a 9-inch baking pan with parchment paper and butter or lightly oil the parchment to prevent sticking.
Mix the cornstarch with water in a small bowl using a fork.
In a small saucepan, combine raspberries, 3 tablespoons of sugar, lemon juice, and the cornstarch mixture. Smash and stir raspberries with a wooden spoon.
Bring the mixture to a boil over medium-high heat and keep boiling for 3 minutes, stirring periodically to prevent burning.
Remove from heat and allow to cool completely before using. After cooling for about 20 minutes, put it in the fridge to chill.
Prepare the Oreo Crust:

Crush the Oreos into crumbs using a blender, food processor, or a gallon ziplock bag with a rolling pin.
In a microwave-safe bowl, melt the butter in the microwave.
Add the finely crushed cookie crumbs to the melted butter and combine well. Pour into the prepared pan and press the mixture down with a measuring cup or your hands.
Cook the crust for 8 minutes. Remove from the oven and set aside. Keep the oven on.
Prepare the Cream Cheese Layer:

In a large mixing bowl with a hand mixer or the bowl of a stand mixer, add in cream cheese and beat until smooth, scraping the bowl as needed.
Add sugar, eggs, and vanilla, and mix until smooth.
Once the Oreo crust has cooled some, pour in the cheesecake batter and spread it out with a spatula.
Drop spoonfuls of the raspberry sauce over the cream cheese mixture. To make swirls, draw a knife back and forth through the cheesecake and the raspberry topping.
Bake and Chill:

Bake cheesecake bars for 35-40 minutes until the edges are just turning golden brown. To prevent the cheesecake from cracking, leave it in the oven with the heat turned off and the door open.
Cover the cooked cheesecake with aluminum foil and refrigerate for at least 2 hours.
Cut into small squares or rectangular bars and enjoy!