Preheat oven to 350°F (175°C). Line baking sheets with parchment paper or silicone liners.
Whisk together the flour, baking powder, baking soda, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter, sugar, and brown sugar until light and fluffy. Add the eggs, one at a time, mixing well after each addition. Mix in the vanilla.
Reduce mixer speed to low. Gradually add the flour mixture, mixing just until combined or a few small streaks of flour remain.
Gently stir in the chocolate chips and cherries.
Scoop the dough by 3-tablespoon portions and roll into balls. Place onto the prepared pans, leaving about 2 inches between cookies.
Bake, one pan at a time, 15-18 minutes, or until the edges of the cookies are just browned and the centers are a bit soft. Use a cookie spatula or a flat-bottomed glass to flatten the tops of the cookies while they're still warm.
Cool the cookies on the pan for 5 minutes. Then transfer the cookies to a wire rack to cool completely.
Notes
*Freeze-dried fruits are usually found alongside the dried fruits. As an alternative with a little different flavor and texture, you can use dried cherries.
Store in an airtight container at room temperature up to 5 days.