In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese on medium speed until smooth, 1 to 2 minutes. Add the powdered sugar and vanilla, and beat on low speed until combined, about 30 seconds. Scrape the sides and bottom of the bowl with a rubber spatula. Increase the speed to medium, and beat until smooth, 1 minute more.

Scrape the sides and bottom of the bowl. Add 1 cup of the heavy cream, and beat on low speed until smooth. Add the remaining 2 cups of heavy cream, increase the speed to medium high, and beat until soft peaks form, 1 to 2 minutes.

Spoon ¼ cup of the cream mixture into the bottom of a 9-inch square baking dish, smoothing into a thin, even layer.

Top the cream mixture with a single layer of cookies, breaking some as needed to fit. Spread about 1 ½ cups of the cream mixture over the cookies, smoothing into an even layer with a spoon or offset spatula. Top with an even layer of raspberries from 2 (6-ounce) containers. Add another 1 ½ cups of the cream mixture, smoothing into an even layer. Top with a final layer of cookies, then add the remaining cream mixture on top, smoothing into an even layer.

Cover with plastic wrap and refrigerate for at least 4 hours or up to 12 hours.

Decorate the cake as desired with crumbled cookies and the remaining raspberries. Use a serrated knife to slice and serve.