Set the oven to 400°F (205°C). Grease a muffin tin with butter or nonstick spray. On a floured surface, roll out the chilled pie dough to an even thickness. Using a round cutter, stamp out circles that are a bit larger than the muffin cups. Fit each dough circle into a cup, allowing the edges to pleat naturally for a rustic appearance.
In a medium mixing bowl, whisk together the pumpkin puree, condensed milk, eggs plus extra yolk, cinnamon, ginger, nutmeg, and salt. Stir gently until the mixture is smooth and uniform; do not overbeat, as that will introduce air bubbles and make the filling frothy.
Pour the filling into the prepared crusts, stopping slightly below the rim to leave room for expansion during baking.
Place the muffin tin in the preheated oven and bake for 10 minutes at 400°F (205°C) to set the crust and begin cooking the filling. Then lower the oven temperature to 325°F (165°C) and continue baking for another 10 minutes. Should the crust edges start to over-brown, shield them with a loose piece of aluminum foil.
Remove the mini pies from the oven and set the tin on a wire rack. Let them cool for a minimum of 10 minutes so the filling can set properly before you serve them.