In the bowl of an electric mixer fitted with a paddle attachment, mix together the butter and 1 cup of sugar until they are just combined. Add the vanilla. In a medium bowl, sift together the flour and salt, then add them to the butter-and-sugar mixture. Mix on low speed until the dough starts to come together. Dump onto a surface dusted with flour and shape into a flat disk. Wrap in plastic and chill for 30 minutes.
Roll the dough 1/2-inch thick and cut with a 3 by 1-inch finger-shaped cutter. Place the cookies on an ungreased baking sheet and sprinkle with sugar. Bake for 20 to 25 minutes, until the edges begin to brown.
Put 3 ounces of the chocolate in a glass bowl and microwave on high power for 30 seconds. Stir with a wooden spoon. Continue to heat and stir in 30-second increments until the chocolate is just melted. Add the remaining chocolate and allow it to sit at room temperature, stirring often, until it's completely smooth. Drizzle 1/2 of each cookie with just enough chocolate to coat it.