Preheat oven to 350 degrees. Place softened butter in a mixing bowl. You'll need to whip using a whisk for about 5 minutes. I recommend using an electric mixer. The goal is to get it to look like whipping cream.
While the butter is whipping, lay the cherries on a napkin to dry. Gently press with a napkin over the tops to absorb more moisture.
After about 5 minutes, add the sugar, almond flavor, cornstarch and flour to the butter and continue whisking to combine. Beat on high for 3-4 additional minutes.
Scoop out a tablespoon of dough, stick your thumb into the center and place your dry cherry inside.
Roll the dough around the cherry so that it's completely covered. Try to get the cookie nice and round.
Place the cookie dough balls onto a prepared baking sheet and bake for 12-14 minutes at 350 degrees F. Cook until lightly browned on the bottoms.
Remove from oven and let cool for a few minutes before transferring to a cooling rack.
While the cookies cool, prepare the icing.