For the Cookies: In a large bowl, beat the butter, sugar, vanilla, cinnamon, and salt with an electric mixer until light and fluffy, about 2 minutes. Beat in the egg. Stir in the flour until just blended. Mix in the apricots, almonds, and pine nuts.
Transfer the dough to a sheet of plastic wrap and shape into a log, about 12-inches long and 1 1/2-inches in diameter. Wrap the dough in the plastic and refrigerate for 2 hours.
Preheat the oven to 350 degrees F. Line 2 heavy baking sheets with parchment paper.
Cut the dough log crosswise into 1/4 to 1/2 inch-thick slices. Transfer the cookies to the prepared baking sheets, spacing evenly apart. Bake until the cookies are golden around the edges, about 15 minutes. Transfer the cookies to a wire rack to cool completely before icing.
For the Icing: Place the confectioners' sugar in a medium mixing bowl. Gradually whisk in the almond flavored liqueur, until the mixture is of drizzling consistency.
Place the wire rack over a baking sheet. Using a spoon or 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 30 minutes.