Prepare a grill for medium indirect heat: For gas grills (with 3 or more burners), turn all the burners to medium-high heat; after about 15 minutes turn off one of the middle burners and turn the remaining burners down to medium. For charcoal grills, bank one chimney starter-full of lit and ashed-over charcoal briquettes to one side of the grill. Set up a drip pan on the other side to avoid flare-ups. (Be sure to consult the grill manufacturer's guide for best results).
Meanwhile, gently whisk the pumpkin, cream, granulated sugar, cinnamon, nutmeg, vanilla, salt and 2 eggs together in a large bowl. Beat the remaining egg in a small bowl and brush on the crust edge. Pour the filling into the crust. Place the pie on the indirect heat side of the grill. Cover and cook until it is starting to set around the edges, about 25 minutes, then rotate, cover and cook for another 25 minutes (the middle will still jiggle slightly). Move the pie to the direct heat side of the grill and cook for 3 more minutes to help crisp the bottom of the pie. Transfer to a rack; let cool completely.