Preheat your oven to 350 degrees F.
In a mixing bowl, beat butter until it’s light and creamy.
Add the sugar and powdered sugar to the bowl and beat until well combined.
Now, pour in the vegetable oil and add the eggs. Mix until everything is well combined.
Next, add the dry ingredients: cornstarch, cream of tartar, baking soda, salt, and cocoa powder. Mix until just combined.
Now, gradually add the flour to the mixture.
Using an ice cream scoop, scoop out the cookie dough and gently roll it into a ball shape.
Prepare your glass with a flat bottom. Moisten it lightly with water.
Dip the bottom of the glass into the reserved additional sugar, then gently press it into the center of each cookie.
Bake the cookies in your preheated oven for approximately 9 minutes.
Remove the cookies from the oven and immediately press the bottom of the glass into each indentation again while they are still hot.
Allow the cookies to cool completely on the baking sheet.
While the cookies cool, melt the white chocolate chips according to the package directions.
Stir in the crushed candy canes into the melted chocolate.
Spoon the peppermint bark mixture into the indented wells on each cookie.
