Preheat the oven to 325°F (165°C). Line two baking sheets with parchment paper and set aside.

In a large mixing bowl, combine the softened butter, powdered sugar, and salt. Using a hand mixer or stand mixer, beat the mixture until light and fluffy, scraping down the sides of the bowl as needed.

Gradually add the all-purpose flour to the butter mixture and mix until fully incorporated and a soft dough forms.

Stir in the butterscotch chips and finely chopped pecans until evenly distributed throughout the dough. Mixing by hand is recommended to ensure even incorporation without overworking the dough.

Using a medium cookie scoop, portion the dough into balls and place them approximately 1 inch apart on the prepared baking sheets.

Bake for 15–20 minutes, or until the cookies are set and firm to the touch. The cookies should remain pale and should not brown.

Remove the cookies from the oven and transfer them to wire racks to cool completely before glazing.

While the cookies are cooling, prepare the rum glaze. In a medium bowl, whisk together the powdered sugar, milk, and rum extract until smooth. Add additional milk, one teaspoon at a time, if a thinner glaze consistency is desired.

Once the cookies have cooled, either dip each cookie into the glaze or spoon the glaze over the tops.

While the glaze is still wet, sprinkle with additional chopped pecans. Allow the glaze to set before serving.