In the bowl of an electric mixer fitted with a paddle attachment, mix together the butter and granulated sugar until they are just combined and 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 1/4-inch thick and cut into flower shapes with a cutter. Place the cookies on an ungreased baking sheet.
Bake for 20 to 25 minutes, until the edges begin to brown. Allow to cool to room temperature.
For the glaze, place the confectioners' sugar in a medium bowl and add about 4 to 5 tablespoons of water until you have a runny, but not too thick frosting. Spread the glaze to the edge of each cookie and garnish the middle of each cookie with a chocolate button.