Preheat the oven to 350 degrees F.
In the bowl of an electric mixer with the paddle attachment, cream 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 roll 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-inch heart-shaped cutter. Place the hearts on an ungreased sheet pan and sprinkle with sugar. Bake for 20 to 25 minutes, until the edges begin to brown. Allow to cool to room temperature.
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