In a large mixing bowl, cream together the softened butter and powdered sugar until light and fluffy, about 2-3 minutes.
Add the instant pistachio pudding mix to the creamed mixture and mix until well combined.
Gradually add in the all-purpose flour and almond extract, mixing until just combined.
Gently fold in the finely chopped maraschino cherries until evenly distributed.
Cover the dough with plastic wrap and refrigerate for at least 30 minutes.
Preheat your oven to 350°F (180°C) and line your baking sheets with parchment paper.
Using a cookie scoop or spoon, portion out the dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, until edges are lightly golden.
Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.