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.
Recipe courtesy of Giada De Laurentiis, 2008