Preheat oven to 300°F.

In a large mixing bowl, beat the butter and shortening with an electric mixer on medium speed for about 30 seconds until combined.

Add granulated sugar, brown sugar, maple syrup, baking soda, cream of tartar, and salt. Beat on medium speed for 2 minutes, scraping the sides of the bowl as needed.

Add egg yolks and vanilla, then beat until combined.

Mix in the flour until a soft dough forms.

Shape dough into 1 1/2-inch balls and place them 3 inches apart on an ungreased baking sheet.

Bake for 12 to 14 minutes or until the edges are lightly browned. The tops will still look slightly soft.

Let cookies cool on the baking sheet for 2 minutes, then transfer them to a wire rack to cool completely. The centers will dip slightly as they cool.

Once cooled, drizzle each cookie with maple icing.

In a small bowl, whisk together the milk, melted butter and maple syrup.

Gradually whisk in powdered sugar until the icing reaches a drizzling consistency.