Roll out pie crust (if your pie crust isn't already in a pie pan) into an 11-inch circle. Place in a 9-inch deep dish pie pan. Fold edges of the crust under each other, and crimp.
Combine brown sugar, ginger, cinnamon, salt, allspice, eggs, pumpkin, and sweetened condensed milk in a bowl using a whisk.
Pour pie filling into prepared pie crust. Place pie on a baking sheet. Bake on lowest oven rack, in bottom third of the oven. Bake at 375F for 40 minutes, until a knife in the center comes out clean. (This may take longer.)
Cool for 1 hour on wire rack. Refrigerate for at least two hours. Top with toasted coconut.