I got this recipe from www.joyofbaking.com. The one thing I needed to do was let them bake longer and make the cookies a bit thicker than the recipe says for high altitude. When slightly browned, (don't over bake or brown), they seem to not break as easily.
2 cups all-purpose flour
1/4 tsp salt
1 cup unsalted butter, room temperature
1/2 cup confectioners sugar
1 teaspoon pure vanilla extract
Beat butter in a bowl with an electric mixer until smooth and creamy. Add sugar and beat until smooth. Add salt and vanilla and blend well. Gently stir in the flour until just incorporated. Flatten the dough into a disk shape and wrap in plastic wrap. Chill for an hour or until firm.
Preheat oven to 350 degrees. Line two baking sheets with parchment paper.
On a lightly floured surface roll the dough into a little more than 1/4 inch thick circle. Cut into rounds or shapes with a lightly floured cookie cutter. Place on prepared baking sheets and place in the refrigerator for about 15 minutes. Bake for 8 - 10 minutes (high altitude for 12) or until cookies are very lightly browned. Cool on a wire rack.
For Chocolate Dipped Shortbread; Place 3 ounces of finely chopped good quality chocolate in a double boiler. After chocolate is just melted and smooth remove from heat. Add 3 more ounces of shaved chocolate and stir with wooden spoon til smooth and glossy. Taking one cookie at a time, dip one end of each cookie in the melted chocolate and place it on a parchment lined baking sheet. Once all the cookies have been dipped in the chocolate, place the baking sheets in the refrigerator for about 10 minutes or until the chocolate has hardened.
Shortbread cookies will keep in an airtight container for about a week or they can be frozen.