Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper.
Mix dry ingredients: In a medium bowl, whisk together flour, baking powder, and salt.
Cream butter and sugar: In a large bowl, beat softened butter and granulated sugar until light and fluffy (about 2–3 minutes).
Add wet ingredients: Beat in the egg, vanilla extract, and almond extract (if using).
Add cherry juice: Mix in the maraschino cherry juice until combined.
Combine wet + dry: Add the dry ingredients to the butter mixture and mix just until no flour streaks remain.
Fold in cherries: Gently stir in the chopped, well-drained cherries.
Scoop cookies: Scoop 1 to 1 1/2 tablespoon portions and roll into balls. Place 2 inches apart on the baking sheet.
Bake: Bake for 10–12 minutes, until the edges are set and the tops look just matte (don’t overbake for soft cookies).
Cool: Let cookies cool on the baking sheet 5 minutes, then move to a rack to cool completely.
Optional glaze: Whisk powdered sugar with milk or cherry juice (start with 1 tbsp and add more as needed). Drizzle over cooled cookies and let set.