Roll out pie dough on a lightly floured surface until it's about 1/4 inch thick.
Cut out circles slightly larger than your mini pie pans. I do this by placing a pan upside down on top of the dough and cutting it 1/2 inch wider all around the pan.
Flip the pan over and place the dough inside of the pan. Line the pie pans with pie crust pushing dough into all the corners and bends.
Trim off any excess dough with a sharp knife.
Repeat with remaining dough and pans.
In a large mixing bowl, combine the brown sugar, flour, salt, cinnamon, allspice, and pumpkin puree. Stir to combine.
Add the egg and mix well to combine.
Stir in the evaporated milk.
Place all of the prepared mini pie shells on a baking sheet.
Use a small measuring cup to pour the pumpkin mixture into prepared pie shells. Fill each shell 1/4 inch from the top.
Bake for 30-35 minutes or until a knife inserted into the middle of a mini pie comes out clean.
Allow the pies to cool for at least 30 minutes before removing them from the tart pans. You can serve these warm or at room temperature.
Serve with a swirl of whipped cream on top if you'd like (you can put the whipped cream in a pastry bag with a large piping tip and pipe it onto the mini pies).
Notes
You'll need one pie crust (a single pie crust) for this recipe. You can make your favorite pie crust recipe from scratch or buy a pre-made pie crust from the store that comes rolled up (don't get the kind that's already shaped in a pie pan).
You can use canned whipped cream, homemade whipped cream piped out like icing, or you can just serve the whipped cream next to the pie and people can put a little on themselves.