Cinnamon Coins

2 sticks ( 1/2 pound) unsalted butter, softened
1/2 cup granulated sugar
2 teaspoons cinnamon
1/4 teaspoon fine sea salt
1/2 teaspoon pure vanilla extract
2 1/2 cups all-purpose flour
Crystallized sugar, for rolling

In a large bowl, beat the butter until creamy. Add the granulated sugar and beat until combined. Beat in the cinnamon, salt and vanilla, then beat in the flour. Divide the dough into thirds; wrap each piece in a large sheet of plastic wrap and shape it into a 10-inch log about 1 1/4 inches thick. Refrigerate until firm, about 1 hour.
Preheat the oven to 350°. Line 3 large baking sheets with parchment paper. Unwrap 1 piece of dough. Sprinkle crystallized sugar into a 3-by-10-inch rectangle on a sheet of wax paper. Roll the log in the sugar, pressing lightly. Cut the log into |-inch-thick slices. Arrange the coins about 1 inch apart on 1 of the prepared baking sheets. Repeat with the remaining 2 logs of cookie dough. Bake the cookies for about 17 minutes, or until golden. Let cool on the baking sheets.