Pulse the cranberries in a food processor 6-8 times until very finely chopped. In a medium bowl, whisk together the flour and baking powder.
Using a hand mixer or stand mixer, cream the butter, brown sugar and salt until smooth and fluffy. Beat in the egg and vanilla. In batches, beat in the flour mixture until just combined. Stir in chopped cranberries.
Transfer dough to a large sheet of plastic wrap and shape into a log about 2 inches in diameter and 10 inches long. Wrap dough tightly and continue to shape dough into smooth cylinder. Freeze 1 hour. Remove from freezer and, in the plastic wrap, roll cookie dough into a smoother cylindrical shape. Return to freezer for 3 hours, until firm.
Preheat oven to 350 degrees F. Unwrap dough and cut into 1/2-inch slices. Arrange on parchment paper-lined cookie sheets, spacing 1 inch apart.
Bake cookies until golden, 10 to 15 minutes, switching racks halfway through. Let cool slightly and transfer cookies to a wire rack set over a large sheet of parchment or wax paper to cool completely.
In a microwave-safe bowl, microwave the white chocolate in 30-second intervals, until melted, stirring in between. With fork, drizzle white chocolate over cookies on rack. Let stand until chocolate sets.