In a large bowl, beat together the softened cream cheese, 1 tablespoon of milk, granulated sugar, and vanilla extract until the mixture is smooth and creamy. Gently fold in 4 oz (half container) of the whipped topping, being careful not to deflate it. Spread this cream cheese mixture evenly into the bottom of the graham cracker pie crust to form the first layer.
In another bowl, whisk together 1 cup of milk, the pumpkin puree, both packages of instant vanilla pudding mix, ground cinnamon, and pumpkin pie spice until thick and creamy with no lumps remaining. Carefully spread the pumpkin mixture over the cream cheese layer in the pie crust. I always make sure to whisk for at least 2-3 minutes to ensure the pudding sets up nicely.
Spread the remaining 4 oz of whipped topping over the pumpkin layer, smoothing it out with a spatula. Refrigerate the pie for at least 4 hours, or until set. For best results, I like to let the pie chill overnight for the flavors to fully blend and the layers to firm up before serving.