In the bowl of a stand mixer fitted with the paddle attachment, whip the butter on high speed for 2-3 minutes, or until it is light and fluffy.
Add the confectioners sugar, vanilla, and salt. Mix again on low speed just until the sugar is fully combined— about 1 minute.
Next, alternate between adding the flour and milk while the mixer is on low speed. First, add half the flour, then half the milk, then the remaining flour, then the remaining milk.
Continue mixing on low speed just until the dough forms a ball around the paddle.
Form the dough into a disk and wrap it in plastic wrap. Refrigerate for 15 minutes.
In the meantime, preheat your oven to 350F. Line two large baking sheets with parchment paper.
Lightly sprinkle your work surface with flour and roll the dough out until it is 1/4” thick.
Use a pumpkin cookie cutter to cut the dough and transfer the cookies to the prepared baking sheet.
Note: I used a cookie cutter that was 2” in diameter. Additionally, make sure to place the cookies at least 1” apart on the baking sheet.
Bake the cookies for 10-12 minutes, or until the edges are just starting to turn golden brown. Set them aside to cool completely.