Preheat your waffle iron according to the manufacturer's instructions. Lightly grease it with cooking spray or butter to prevent sticking.
In a large mixing bowl, combine the softened butter, granulated sugar, and brown sugar. Use an electric mixer to cream the mixture until it’s light and fluffy.
Beat in the egg and vanilla extract until well combined. Make sure to scrape down the sides of the bowl to incorporate all the ingredients.
In another bowl, whisk together the all-purpose flour, baking soda, cinnamon, and salt. Gradually add this mixture to the wet ingredients, mixing until just combined.
Scoop about 2 tablespoons of dough onto the preheated waffle iron. Close the lid and cook for about 3-4 minutes, or until the cookies are golden brown and cooked through. Carefully remove them and transfer to a cooling rack.
In a small bowl, beat together the softened cream cheese, powdered sugar, and vanilla extract. Add heavy cream or milk gradually until you reach a glaze consistency.
Once the cookies have cooled, drizzle the cream cheese glaze over the top. Allow it to set for a minute before serving.