In the bowl of an electric mixer fitted with the paddle attachment, cream together the butter and sugar. Add in the vanilla and salt and continue beating the mixture until it is smooth, scraping down the sides of the bowl as needed with a spatula.
Mix in the flour at low speed to form a dry crumbly mixture, then mix in the milk to bind the ingredients into an even cookie dough. Mix in the chopped crystallized ginger.
Divide the dough in two and roll each half into a log of about 1.5 inches in diameter. Roll each log in turbinado (if using) to coat it evenly all around. Wrap with plastic wrap and chill overnight.
Preheat the oven to 350ºF. Working with 1 log of dough at a time, slice the crystallized ginger cookies fairly thin. Stagger the sliced cookies on a parchment-lined baking sheet and bake them until the edges are golden, about 15 minutes or so. Let cool a couple of minutes before transferring to a rack to cool completely.