Preheat oven to 350 degrees.
In the bowl of an electric mixer fitted with a paddle attachment, mix together the butter and 1 cup of sugar just until they are combined. Add the vanilla. In a medium bowl, sift together the flour and salt, then add them to the butter/sugar mixture. Mix on low speed until the dough starts to come together. Dump dough onto a surface dusted with flour and shape into a flat disk. Wrap in plastic and chill for 30 minutes.
Roll the dough to 1/2 inch thick, and cut with the cookie cutter of your choice (mine was about 1.5 x 3). Place the cookies on an ungreased cookie sheet and sprinkle with sugar. Bake for 20-25 minutes, until the edges begin to brown. Allow to cool to room temperature.
Optional Step (if you want to add a little chocolate to the shortbread). When the cookies are cooled, place them on a baking sheet lined with parchment paper. Put 3 oz. of finely-chopped, high-quality semisweet chocolate in a glass bowl and microwave on high for 30 seconds. Stir. Continue to heat and stir in 30-second increments until the chocolate is just melted. Add an additional 3 oz. of finely-chopped, high-quality chocolate and allow to sit at room temperature, stirring often, until it's completely melted and smooth. Stir vigorously until the chocolate is smooth and cooled slightly (stirring makes it glossier). Drizzle half of each cookie with just enough chocolate to coat it and let harden before serving.
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