Cream together the butter and sugar in a mixing bowl until light and fluffy, about 3-5 minutes. Beat in the egg and vanilla extract. Gradually mix in flour and salt until a soft dough forms. Chill for 30 minutes.

Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper. Roll the dough into 1.5-tablespoon balls and place 2 inches apart. Flatten slightly and create a well in each ball. Bake for 10-12 minutes until golden brown. Press down the wells if necessary after baking.

While the cookies cool, beat the cream cheese in a bowl until smooth. Mix in the pumpkin puree, brown sugar, pumpkin pie spice, cinnamon, vanilla, and heavy cream until blended. Chill in the refrigerator for at least 30 minutes.

Once cool, pipe or spoon the filling into the wells of each cookie. Top with whipped cream and a sprinkle of cinnamon or nutmeg.

Fill the cookies shortly before serving. Store unfilled cookies in an airtight container for up to 4 days. Filled cookies are best enjoyed within 2 days for optimal freshness.