In large bowl, beat butter with sugar until light and fluffy, about 2 minutes. Beat in the egg and vanilla and continue mixing until well combined. In a separate bowl, whisk together flour, baking powder and salt. Stir flour into butter mixture in 2 additions. Stir in cherries.
Divide dough into thirds. Place one piece on a large piece of waxed paper and roll it into an 8-inch (20 cm) long log. Remove paper, wrap in plastic wrap, and twist ends to seal. Repeat with the other two pieces. Refrigerate for at least 3 hours or until firm.*
When ready to bake, preheat oven 375°F. Cut into 1/3-inch (~1 cm) thick slices and place, about 2 inches apart, on parchment paper-lined baking sheets. Bake for about 10 minutes or until lightly browned on the bottom.
Let pans cool on a wire rack for 5 minutes. Transfer to racks and let cool completely.