Preheat the oven to 350°F. Line a 9x9-inch metal baking dish with parchment paper. Set it aside.
Using a small mixing bowl, combine the crushed Oreos and the melted butter.
Press the Oreo mixture into the bottom of the prepared baking dish. Set it aside.
Using either a stand mixer or a medium-size mixing bowl and a handheld mixer on medium-high speed, beat the cream cheese for 1 to 1½ minutes until smooth.
Add in the granulated sugar and continue mixing for 1 to 1½ minutes.
Add the vanilla extract and almond extract, and continue mixing until combined.
Add the eggs, one at a time, mixing well after each egg.
Pour the cheesecake batter on top of the Oreo base. Set it aside.
Cut the prepared cookie dough into four sections. Flatten the dough and lay it on top of the cheesecake layer. Bake for 35 to 40 minutes, until the top is golden brown. Allow the bars to rest for 30 minutes, cover and chill in the refrigerator for 3 hours.
Remove from the fridge and remove from the baking dish by lifting the parchment paper. Place the bars on a large cutting board. Slice into sixteen 2¼-inch x 2¼-inch pieces.