Blind-bake the crust by preheating the oven to 375°F. Place the pie crust into a 9-inch pie plate and crimp the edges. Line it with parchment and fill with pie weights or dried beans. Bake until the edges begin to set, then remove the parchment and weights and continue baking briefly until the bottom looks dry. Let the crust cool completely before adding any filling.
Prepare the cream cheese filling by beating the cream cheese, sugar, and flour until smooth. Add the egg and vanilla and mix until creamy. Scoop out ½ cup of the cream cheese mixture and place it in a separate bowl. Save the remaining mixture to mix into the pumpkin filling. Add the milk a little at a time, only to the reserved ½ cup portion, stirring until it becomes smooth and can be easily swirled into the pumpkin filling.
Make the pumpkin filling by whisking the pumpkin puree, granulated sugar, eggs, pumpkin pie spice, and salt in a mixing bowl. Add the undiluted remaining cream cheese mixture and whisk until the filling becomes extra creamy and fully combined.
Assemble the pie by pouring the pumpkin filling into the cooled crust. Spoon the thinned cream cheese filling over the pumpkin layer and gently swirl it with a knife or skewer, creating decorative ribbons without overmixing.
Bake the pie by lowering the oven temperature to 350°F and placing the pie inside. Bake until the edges are set and the center still has a slight jiggle. Allow the pie to cool at room temperature and then chill it until fully set for easy slicing.