Preheat oven to 325 degrees F.
In a small bowl, using an electric mixer or by hand using a rubber spatula or wooden spoon, beat the butter, sugar, salt and vanilla until well combined. Do not overmix; you don't want the butter to become fluffy. Scrape down the bowl using a rubber spatula and beat for a few more seconds. Sift the flour into the bowl and mix on low speed or by hand just until absorbed. Scrape the bowl with a rubber spatula and mix again for a few seconds. Turn the dough onto the table, gather it together, and knead gently into a smooth mass. The dough can be made ahead and stored in the refrigerator for up to 2 days.
Form the dough into a round patty and quarter into 4 even pieces. Roll each piece into a log and cut each log into 10 even pieces. Roll each piece into a 3/4-inch ball-about the size of a large marble. Place the balls about 1 1/2-inches apart on ungreased baking sheets and flatten gently and evenly with the heel of your hand so that they're about 1/4-inch thick. Bake for 22 minutes, or until the cookies just begin to color and the bottoms are golden. Let sit for 5 minutes, then transfer to a rack to cool completely.
If the ganache was made 2 hours before, it will be soft and moussy. Whisk it a few times to thicken. If the ganache was made earlier in the day or the day before, it will be stiff. Warm it briefly, stirring gently, until it softens a little. Whisk it with 1 or 2 quick strokes.
Be sure the cookies are completely cool. Place the ganache in a pastry bag fitted with a large star tip. Holding the bag in a vertical position about 1/2-inch above the cookies, pipe a large dollop of chocolate, leaving a small border of cookie showing around the edge. Repeat with the remaining cookies. The chocolate will firm up in about 1 hour. To hasten the process, refrigerate the cookies for 5 minutes. Serve at room temperature.Ganache:
In a small pot, scald the cream until bubbles appear around the edge and it's just about to boil. Remove from heat and stir in the chopped chocolate. Stir occasionally until the chocolate is melted and the mixture is smooth and dark. Transfer to a small bowl and set aside to cool until it thickens, stirring occasionally, about 2 hours. The ganache can be made the day before and left covered, at room temperature, overnight.
Recipe courtesy of Peggy Cullen