Preheat oven to 300. In a medium bowl, mix together flour, soda, cinnamon, ginger, and allspice. Mix until blended well. In a large mixing bowl, beat sugar and butter at medium speed until mixture forms a grainy paste and scrape sides of bowl. Add molasses and egg and beat until light and fluffy. Add flour mixture and apricots and blend at a low speed just until combined. Do not overmix. Divide dough in half and shape each half into a roll about 1 1/2 inches in diameter. Wrap rolls in waxed paper and chill until firm. Slice cookies 1/2-inch thick and place on ungreased cookie sheets about 2 inches apart. Bake 25-30 minutes until cookies are set. Transfer to cool surface.

Icing: blend sugar, milk, and extract in a small bowl until smooth. Drizzle cookies with icing.