Preheat the oven to 350 degrees F (175 degrees C). Spray an 8-inch glass baking dish with cooking spray.

Place cream cheese in the bowl of a stand mixer fitted with the paddle attachment; beat on high speed until smooth. Add pumpkin puree, eggs, sweetener, pumpkin pie spice, cinnamon, and vanilla extract. Beat well. Pour batter into the prepared dish.

Bake in the preheated oven until center is set, about 40 minutes. Cool to room temperature before serving, or serve cold.