In a large bowl, with an electric mixer, beat the butter, sugar, vanilla extract, almond extract, cinnamon, and salt until light and fluffy, about 2 minutes, then beat in the egg.
Add the flour and beat on the lowest speed until just blended.
Using a wooden spoon, stir in the dried cherries and almonds.
Transfer the dough to a sheet of plastic wrap and shape it into a log, about 12-inches long and 1 ½-inches in diameter.
Wrap the dough in the plastic wrap and refrigerate for at least 2 hours. (Dough can be made up to 3 days in advance).
Arrange an oven rack in the center of the oven. Preheat the oven to 350 degrees F. Line 2 heavy baking sheets with parchment paper.
Cut the log crosswise into ½-inch thick slices.
Transfer the dough slices to the prepared baking sheets, spacing them about 1-inch apart.
Bake until the cookies are golden around the edges and puffed, about 15 minutes.
Transfer the cookies to a wire rack to cool completely before icing, about 30 minutes.
Put the powdered sugar in a medium bowl. Gradually whisk in the vanilla extract and water, adding more water, 1 teaspoon at a time, until the mixture becomes a drizzling consistency.
Put the cooled cookies on a wire rack set over a baking sheet.
Using a spoon or a fork, drizzle the cookies with the icing, allowing any excess icing to drip onto the baking sheet.
Allow the icing to set before serving, about 1 hour.