Preheat your oven to 400°F (200°C). Line two large baking sheets with parchment paper.
In a large bowl, use an electric mixer to beat the softened butter until it's smooth and creamy. Add 1/2 cup of powdered sugar and continue to beat until the mixture is light and fluffy. Mix in the almond extract.
In a separate medium bowl, whisk together the flour and salt.
With the mixer on low speed, gradually add the flour mixture to the butter mixture. Mix just until a dough forms. Use a spatula to stir in the finely chopped candied cherries.
Shape the dough into 1-inch balls and place them about 2 inches apart on the prepared baking sheets.
Bake for 9 to 11 minutes, or until the bottoms of the cookies are just lightly browned. Let the cookies cool on the baking sheet for about 5 minutes; they will be fragile.
While the cookies are still warm, place the remaining 1/2 cup of powdered sugar in a small bowl. Gently roll each warm cookie in the sugar to coat. Transfer the coated cookies to a wire rack to cool completely.
Once the cookies are cool, place the chocolate chips in a small, microwave-safe bowl. Microwave in 20-second intervals, stirring between each, until the chocolate is melted and smooth. You can also melt the chocolate in a small resealable bag and snip off a corner.
Drizzle the melted chocolate over the cookies. Let the cookies stand at room temperature for at least 30 minutes for the chocolate to set before serving or storing.