Preheat your oven to 375°F and line your cookie sheets with parchment paper.

In a large mixing bowl, cream together the softened butter, vegetable oil, sugar, and powdered sugar until light and fluffy.

Add the eggs, one at a time, mixing well after each addition, then beat in the vanilla and peppermint extracts.

In a separate bowl, whisk together the flour, baking soda, and cream of tartar.

Gradually combine the dry ingredients into the wet mixture until well incorporated.

Using a cookie scoop or tablespoon, drop the dough onto the prepared sheets, leaving space for spreading.

Bake the cookies in the preheated oven for about 8-10 minutes, or until the edges are just starting to brown.

While the cookies cool, prepare the icing by mixing the melted butter, vanilla, peppermint extract, and milk into the powdered sugar until smooth.

Drizzle the icing over each cooled cookie and generously sprinkle with crushed peppermint candies.