Preheat oven to 350°F. In a large bowl, cream butter, sugar, and brown sugar together for 2–3 minutes until light and fluffy. Add eggs and vanilla and beat for another 2–3 minutes.
In a separate bowl, whisk together flour, baking soda, and salt. Gradually add dry ingredients to the wet mixture and stir until just combined. Fold in cinnamon chips.
Use a cookie scoop to portion dough onto a parchment-lined baking sheet. Bake for 10–12 minutes, or until edges are golden brown.
Let cookies cool on the pan for a few minutes, then transfer to a wire rack to cool completely before frosting.
To Make the Icing
In a small bowl, beat melted butter, shortening, powdered sugar, milk, and vanilla until smooth.
Spread icing over cooled cookies. This vanilla frosting for cinnamon cookies complements the flavor and adds a beautiful bakery-style finish.