Beat the softened butter and 1/2 cup powdered sugar together until light and fluffy, about 2 minutes. Scrape the bowl down a couple of times so nothing sticks unmixed at the edges.

Mix in the vanilla and cinnamon until just combined.

Add the flour and salt and mix on low until the dough just comes together. It should look soft and a little crumbly, not wet. If it feels dry and won't hold together when you squeeze a bit in your hand, work in another tablespoon of softened butter rather than adding water or milk.

Gather the dough into a ball, cover it, and chill for at least 1 hour. This keeps the cookies round instead of flat.

Preheat the oven to 350F and line a baking sheet with parchment. Roll the dough into 1-inch balls and place them 2 inches apart. Bake for 10 to 12 minutes, until the bottoms are just turning golden.

Let the cookies sit on the pan for about 5 minutes to firm up.

Mix the remaining 1 cup powdered sugar with a little extra cinnamon if desired. Roll the warm cookies in the mixture while they're still a little warm, then let them cool completely and roll a second time for full coverage.