Preheat the oven to 375°F. Line two baking sheets with parchment paper.
To make the dough: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cane sugar, powdered sugar, vanilla extract, and cinnamon. Mix on low until combined.
Add the eggs and the dry ingredients: flour, baking soda, and sea salt in that order. Mix until combined into a stiff dough.
Using your hands, form the dough into 18 balls and place on the prepared baking sheets. Flatten them slightly so they are about 2-inches in diameter.
Bake for 13 to 15 minutes or until lightly golden brown around the edges and cracked and set in the middle. Allow to cool completely on the baking sheets.
To make the icing: In the bowl of a stand mixer fitted with the paddle attachment, add the powdered sugar, butter, and heavy whipping cream, and vanilla extract. Mix on low until combined, then speed mixer up to high for 1 minute or until the icing is light and fluffy.
Using a butter knife, spatula, or a piping bag if you like, frost each cookie with icing. Sprinkle them with holiday sprinkles or decorations.
Store in an airtight container for up to 7 days.