Let cold butter sit at room temperature for about 15 minutes. Drain and chop the cherries; set aside.
Preheat oven to 325 degrees.
In a large mixing bowl, combine flour and sugar. Cut in the butter with a pastry blender or fork. After the butter/flour mixture is crumbly, add the cherries, almond extract, 2/3 cup white chocolate, and food coloring. It will still be really crumbly, but don't panic. Knead for a few minutes till the dough becomes smooth.
Roll dough into 1" balls and place on baking sheets. Use the bottom of a glass dipped in sugar to flatten each of the balls out.
Bake at 325° for about 10-12 minutes. Cool completely on wire racks.
In a small glass bowl, melt the shortening in the microwave. Add the 1 1/3 cups white chocolate. Microwave at half power, stirring every 30 seconds, till smooth.
Dip half of each cookie in the melted chocolate and place on waxed paper or silicone pan liners till chocolate sets up.