Preheat oven to 425°F.
Whisk together pumpkin puree, egg yolks, and egg in a large bowl until smooth. Add sweetened condensed milk, salt, and all of the spices, and whisk until combined.
Prepare a 9-inch pie plate with an unbaked pie crust and crimp the edges to decorate.
Pour the filling into the pie shell and lightly tap the plate on a flat surface to release any air bubbles.
Wrap the edges in foil or a pie protector and bake at 425°F for 15 minutes.
Remove the foil/pie crust protector and continue to bake at 350°F for 30-40 more minutes, until the middle is just set. The tip of a knife inserted about 1 inch from the crust will come out clean.
Allow to cool completely before serving.