Make the Cookies:
In a large bowl or the bowl of a stand mixer, beat together the softened butter and granulated sugar until light and fluffy. Add the eggs one at a time, mixing well after each addition. Add the vanilla extract and mix until combined.
Add the flour, baking powder, cinnamon, and sea salt to the wet ingredients. Mix until a firm dough forms. If the dough is too sticky, add an extra tablespoon or two of flour, but be careful not to overmix. Chill the dough for 30 minutes.
Preheat your oven to 375°F (190°C). Roll the dough into 1-inch balls and place them on baking sheets lined with parchment paper. For extra cinnamon flavor, you can roll the dough balls in cinnamon sugar before placing them on the baking sheets. Flatten each ball slightly with your hand or the bottom of a glass to a thickness of about 1/3 to 1/2 inch.
Bake the cookies for 7 to 8 minutes, or until the bottoms are just barely golden. Be careful not to overbake. Transfer the cookies to a cooling rack and allow them to cool completely before frosting.
Make the Frosting:
In a large bowl, beat together the softened cream cheese and butter using an electric mixer until light and fluffy. Gradually beat in the powdered sugar until smooth. Add the vanilla extract and enough milk or cream to reach the desired consistency, and continue to beat until the frosting is light and fluffy.
Pipe the frosting onto the cooled cookies in a spiral shape using a piping bag fitted with a 1M tip, or by snipping off the corner of a zip-top bag. Sprinkle the tops with ground cinnamon or cinnamon sugar.
Serve and Store:
Store the cookies in a covered container for up to 3 days. Enjoy these delicious cookies with a warm cup of coffee or tea!