Rinse quinoa (to remove any bitterness). Combine 1 cup water and quinoa in a medium saucepan; bring to a boil. Cover, reduce heat, and simmer 20 minutes or until liquid is absorbed. Remove from heat; fluff with a fork, and set aside.
Combine Bisquick and next 4 ingredients (through salt) in a bowl; make a well in center of mixture. Combine milk, molasses, and egg in a separate bowl, stirring well. Add milk mixture, quinoa, and apricots to dry ingredients; stir just until moist.
Spoon batter into two 12-cup muffin pans coated with cooking spray (leave two cups empty in each pan), filling cups half full. Bake at 400° for 12 minutes. Remove from pans immediately; cool.