Cream butter and powdered sugar in the bowl of a stand mixer (or using a hand mixer). Add vanilla and mix, scraping the bowl a few times to make sure that the butter and powdered sugar are completely incorporated. Mix in salt and flour until combined, then stir in the ginger. Note about the ginger: you can muddle the ginger before adding it or not, your choice. I did a combination of both.
Turn out dough onto a sheet of waxed paper. Form dough into a 9” log and roll up in the wax paper sheet. Chill for 30 minutes.
Preheat oven to 350°F. Line a cookie sheet with parchment paper or a silpat baking mat.
Unroll the log of shortbread dough and slice into 18 rounds. Place cookies on prepared cookie sheet (they will not spread much).
Bake for 9-12 minutes, until they start to turn golden, depending on how soft you want them. I cooked mine 10 minutes for a pillowy soft shortbread, but if you want it more cooked then bake them an additional 2 minutes or so. Cool completely before dipping.
To dip, melt chocolate in a small bowl according to package directions. Dip half of each cookie in the chocolate and place it on a wax paper (or silpat) lined cookie sheet. Chill to set. Store cookies at room temperature for up to 3 days or freeze for up to one month.