Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, beat the room-temperature butter, solid shortening, and granulated sugar with an electric mixer until smooth and creamy.
Mix in the almond extract until combined.
Add the all-purpose flour and mix on low speed until a soft dough forms, scraping the bowl as needed.
Shape the dough into 1-inch balls and place them on the prepared baking sheets about 2 inches apart.
Bake for 8 to 10 minutes, until the edges are set but the centers are still soft.
If using maraschino cherries, press half of a cherry into the center of each cookie immediately after removing from the oven.
Let the cookies cool on the baking sheet for several minutes, then transfer to a wire rack to cool completely.