In the bowl of a stand mixer fitted with a paddle attachment or in a large mixing bowl with an electric hand mixer, cream together unsalted butter, powdered sugar, salt, and almond extract.
Add all-purpose flour and mix on low speed until the mixture becomes crumbly.
Add in chopped maraschino cherries and mix on low speed until the dough forms.
Place dough on a sheet of parchment paper. Form the dough using your hands and the parchment paper into a log about 2 inches in diameter. Chill the dough log for at least 1 hour.
Preheat oven to 350° F and line a baking sheet pan with a silicone baking mat or parchment paper.
Slice the cookie dough log into ½ inch pieces. Place the cookies on the pan allowing some room for spreading. Bake for approximately 12-14 minutes until the edges are set and before the cookies start to brown.
Remove the pan from the oven. Cool the cookies on the pan for 2 minutes. Transfer to a wire rack to cool completely.