Preheat oven to 325°F (165ºC). Line a large baking sheet with parchment paper.
In a medium bowl, whisk together flour, sugar, cornstarch and salt.
In a large bowl, combine butter and oil. Beat with a mixer at medium speed until well blended, about 2 minutes.
Beat in vanilla. Add flour mixture; beat at medium-low speed until a firm dough forms.
Divide dough in half. Pat each dough half into a 5 ½-inch circle on a prepared baking sheet.
Using a large knife, cut each circle into 12 wedges, but do not pull wedges apart (keep the circle intact).
Bake at 325°F until just starting to brown around edges, 32–35 minutes.
Immediately re-cut wedges and keep circles intact. Cool cookies completely on pan, about 30 minutes. Space wedges apart.
Place chocolate chips in a small microwave-safe bowl. Microwave on high until chocolate melts, about 1 minute, stopping to stir every 20 seconds.
Scrape the chocolate into a small zip-top plastic bag. Snip a small hole in one bottom corner of the bag; pipe chocolate evenly over cookies.
Sprinkle crushed candy canes over cookies. Let stand until set.
