Cream together butter and sugar until light and fluffy, about 2 minutes. Add flour, cornstarch and salt and mix until just combined.
Form dough into a rectangle on a large piece of plastic wrap and wrap tightly. Refrigerate for an hour (or up to 24 hours).
Preheat oven to 350 degrees F. Line cookie sheets with parchment paper. Remove dough from refrigerator and allow to soften a bit if it was refrigerated for more than an hour. Divide dough in half and roll to 1/4-inch thickness. Cut with a 3-inch cookie cutter. Using the large end of a piping tip, cut out the center. Place on prepared cookie sheets. Bake for 8 minutes.
Remove from oven and allow to cool on the pan for 1 minute. Slide parchment (with the cookies still on it) off of the cookie sheet and allow cookies to cool completely on the counter.
Once cookies are cooled, melt the chocolate chips in the microwave in 30 second increments until just melted. Place parchment paper back onto the cookie sheets. Dip the bottom of the cookies in the melted chocolate and place on the parchment.
Place remaining chocolate in a zip top bag and just barely snip the corner. Drizzle the chocolate back and forth over the cookies to make the stripes. Place cookies in the refrigerator for 15 minutes to allow the chocolate to set up. Store in an airtight container on the counter.