Preheat the oven to 425°F (220°C). Fit pie crust into a 9-inch pie dish and place it on a baking sheet.

Combine pumpkin puree, condensed milk, eggs, and pumpkin pie spice in a large bowl. Mix until combined and set aside.

Make the cheesecake swirl: In a medium, microwave-safe bowl stir together mascarpone, milk, maple syrup, and flour. Microwave on high power until the cheese is completely melted, 20 to 30 seconds. Stir the mixture until completely smooth to make swirling easier.

Add about two-thirds of the cheese mixture into the pumpkin filling and stir to combine. Pour the pumpkin filling into the pie shell. Spoon the remaining mascarpone mixture on top in about 10 or so dollops. Use a thin knife or toothpick to swirl the cheesecake dollops into the pumpkin pie filling to create a swirl pattern.

Bake in the preheated oven for 15 minutes at 425°F (220°C). Reduce heat to 350°F (175°C) and continue to bake until filling is set around the sides but jiggles like jello in the center, for 30 to 35 minutes.

Turn the oven off, open the oven door, and let cool for one hour in the oven before transferring into the fridge to cool completely.