In a bowl with an electric mixer, cream the butter with the sugar until the mixture is light and fluffy. Add in extracts.
Add flour, baking powder and salt. Beat until it forms a dough. Stir in cherries and coconut.
Divide the dough in half. On a sheet of wax paper, form each half into an 8-inch log. Chill the logs, wrapped in the wax paper, for at least 4 hours or overnight.
Heat the oven to 300°F.
Cut the logs into ¼-inch-thick slices with a sharp knife.
Arrange the slices 2 inches apart on parchment-lined baking sheets. Top with one or two almond slices and a sprinkle of turbinado sugar.
Bake the cookies on the top rack of the oven for 25 to 30 minutes, or until they are pale golden.
Transfer to wire racks to cool.