Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a medium bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg. Set aside.

In a large bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.

Beat in the eggs one at a time, then stir in the vanilla extract.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in the butterscotch chips.

Drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart.

Bake for 10-12 minutes, or until the edges are lightly golden. Remove from the oven and let cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.

For the frosting, beat the softened butter in a medium bowl until creamy. Gradually add the powdered sugar, mixing until smooth.

Stir in the butterscotch sauce and vanilla extract. If the frosting is too thick, add milk one tablespoon at a time until desired consistency is reached.

Once the cookies are completely cool, frost them with the butterscotch frosting and enjoy!