Preheat the oven to 350°F and prepare a few baking sheets with parchment paper or line with a silicone mat.
Make the dough. In a large bowl or stand mixer, beat butter and sugar for a couple of minutes until smooth.
Add eggs and vanilla. Beat well, scraping the sides and bottom of the bowl.
Use a cookie scoop or a spoon to shape the dough. You want dough balls about 1 and 1/2 to 2 inches across.
Roll the cookies. In a small or medium bowl, combine sugar and cinnamon. Stir together. Roll the shaped cookies in the cinnamon sugar to coat. (Reserve the remaining cinnamon sugar!)
Place cookie dough balls on the prepared baking sheet with about 2 inches in between them and gently press down. These cookies only spread a little in the oven and must be pressed down.
Bake the cookies at 350 for about 10-11 minutes; the cookies will crack slightly in the oven. Let the cookies set on the pan for at least 3-5 minutes. Remove the cookies to a wire cooling rack and let cool for a few minutes.
While the cookies are still warm but cool enough to handle (and not falling apart), place each cookie back into the bowl of cinnamon sugar*. Coat one side of the cookie, then flip it over and coat the other side. This gives you the ultimate cinnamon-sugar edge to your snickerdoodle! Enjoy one right away with a glass of milk!