Preheat the oven to 425 degrees F. Fit the eggless pie crust into a 9-inch pie pan, shape the edge, and refrigerate it while preparing the filling.
Place the pumpkin puree, sweetened condensed milk, heavy cream, cornstarch, brown sugar, cinnamon, ginger, nutmeg, cloves, fine salt, and vanilla in a blender.
Blend the filling for 30 to 45 seconds, until completely smooth and free of cornstarch lumps. Pour it into the chilled pie crust.
Bake the pie at 425 degrees F for 15 minutes. Reduce the temperature to 350 degrees F and continue baking for 45 to 55 minutes.
Remove the pie when the edges are set and the center has a gentle wobble rather than a liquid ripple. Cover the crust edge loosely with foil if it browns too quickly.
Cool the pie at room temperature for 2 hours. Refrigerate it for at least 4 hours, preferably overnight, so the eggless filling becomes creamy and neatly set.