Beat the softened butter and sugar in a large bowl until light and fluffy, about 2 minutes, then beat in the vanilla.
Whisk the flour and salt together, add to the butter mixture, and mix on low just until a soft dough forms; do not overmix.
Flatten the dough into a disk, wrap it, and chill for 20 minutes.
Heat the oven to 325°F and line two baking sheets with parchment paper.
Roll the dough into 24 one-inch balls, place them 2 inches apart on the sheets, and flatten each to 1/2 inch with the tines of a fork.
Bake 18-20 minutes, until the edges are pale golden; transfer the cookies to a rack and cool completely.
Melt the chocolate in 30-second microwave bursts, stirring between each; dip half of each cooled cookie in the chocolate and return it to the parchment.
Let the chocolate set at room temperature for about 20 minutes, or 5 minutes in the fridge, before storing.
