Begin by preheating your oven to 350°F (175°C). Line a 9x9 inch baking pan with parchment paper, allowing some overhang for easy removal later.
In a medium bowl, combine the melted butter and the room temperature butter. Add the brown sugar, granulated sugar, and salt, mixing until well combined. Then, stir in the vanilla extract. Gradually add the flour and mix until just combined. Fold in the mini chocolate chips and 1 cup of the crushed Oreos.
Press half of the cookie dough mixture into the prepared baking pan. This will be the bottom layer of your bars.
In another bowl, beat the cream cheese until smooth using an electric mixer. Add the granulated sugar, egg, and vanilla extract, mixing until fully combined and creamy. Gently fold in the remaining 1/4 cup of crushed Oreos.
Spread the cheesecake mixture evenly over the cookie dough layer in the pan. Then, crumble the remaining cookie dough over the top of the cheesecake layer, spreading it out as evenly as possible.
Bake the bars in the preheated oven for 25-30 minutes, or until the edges are lightly golden and the center is set but still slightly jiggly. Remember that they will continue to firm up as they cool.
Allow the bars to cool in the pan on a wire rack for about 30 minutes, then transfer to the refrigerator to chill for at least two hours. Once chilled, use the parchment paper to lift the bars out of the pan, and slice them into squares.