In a small bowl, whisk together the flour and salt.
In a stand mixer fitted with the paddle attachment (or using an electric mixer), cream the butter, sugar and vanilla in a stand mixer on medium-high speed until light and fluffy, 3-5 minutes. Lower the speed, and slowly add the flour and half of the chopped Butterfinger candy until the dough is combined.
Flatten the dough into a disc and wrap in plastic film, then chill for at least an hour, or until the butter firms up.
Line a large sheet pan with parchment paper. Place the dough on a lightly floured surface or between two sheets of parchment paper (my preference), then roll out the dough to around 1/4-inch thick. Using a 2 1/4-inch cookie cutter (or similar), portion the dough and place on the prepared sheet pan. Roll the excess scraps in a ball and repeat the process until all the dough is used.
Chill the dough for at least 30 minutes. Meanwhile, preheat the oven to 350 degrees F.
Make sure the cookies are spread at least 1/2-inch apart (they won't spread much). Bake for 10-15 minutes or until lightly golden on top. Allow to cool to room temperature.
Melt the chocolate and half-and-half over a double boiler, stirring until evenly combined. Spread a thin layer of chocolate on top of each cookie and sprinkle the remaining chopped Butterfingers on top, lightly pressing it to adhere. The chocolate will firm up once it reaches room temperature (you can place in the refrigerator to speed up the process).
Store cookies in an airtight container at room temperature, and enjoy within 1 week.