Preheat oven to 325°F.
Cream butter, sugar, ground ginger and allspice until light and fluffy. Beat in eggs, molasses and chopped ginger root. Combine flour, baking soda and salt; blend into butter mixture. Mix in almonds and apricots. (Chill dough for ease of handling.)
Divide dough in half. On a lightly floured surface, shape each portion into two 12-inch long logs. Place logs on a lightly buttered or parchment lined cookie sheet.
Bake 30-35 minutes or until firm. Cool and cut diagonally into 3/8-inch slices. Place slices on a cookie sheet and bake at 250°F for approximately one hour to dry the biscotti.