For the Cookies:
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 1/2-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 1/2-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.
For the Icing:
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. (Makes about 2/3 cups icing, enough to ice both variations.)
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.
To toast the almonds, arrange them in a single layer on a baking sheet. Bake in a preheated 350 degree F oven for 6 to 8 minutes until lightly toasted. Cool completely before using.