Make the Cookies:

Bring your eggs to room temperature by placing them in a glass of warm water for around 10 minutes. Meanwhile, in a small, microwaveable bowl, add 1 cup of chocolate chips and the oil. Microwave in 15-30 second intervals, stirring between each, until the chips are melted and smooth; set aside.
In the bowl of a stand mixer fitted with the whisk attachment, add the room temperature eggs and sugar. Whisk on medium-high until thick, fluffy, and light in color, about 5 minutes (the mixture shouldn’t feel grainy when rubbed between two fingers). Whisk in the peppermint extract.
Remove the bowl from the stand mixer and add the melted chocolate. Use a large spatula to gently fold the chocolate into the egg/sugar mixture until totally combined.
Sift in the cocoa powder, flour, baking powder, and salt. Gently mix until a brownie batter forms. Allow the batter to sit at room temperature, uncovered, for 30 minutes to thicken. This allows the batter to stiffen into a dough that can easily be handled.
Meanwhile, preheat your oven to 350°F and line a baking sheet (or two) with parchment paper.
Once the cookie dough is ready, scoop dough balls (6-8 per baking sheet) 2 Tbsp in size (roughly 41g per dough ball). Roll the dough balls smooth.
Bake at 350°F for 7-9 minutes. Allow the cookies to rest on the baking sheet for 2 minutes before removing to a cooling rack to cool completely.
Decorate the Cookies:

Once the cookies are totally cool, you can melt the chocolate. In a small, microwaveable bowl, add the 1/3 cup of chocolate chips. Microwave in 15-30 second intervals, stirring between each, until the chips are melted and smooth.
Add the melted chocolate to a piping bag (fitted with a small round tip, if desired) or ziploc bag. Snip the corner of the bag and drizzle the chocolate over the cookies.
Immediately top the drizzled cookies with the crushed candy cane and sprinkles. The chocolate will begin to set after about 20-30 minutes, so don’t wait to add the toppings.
Allow the chocolate to set before storing cookies in an airtight container at room temperature. I recommend adding a parchment paper layer between cookie layers to keep the cookies looking their best.