Fruit base: In a saucepan, combine sugar, cornstarch, cinnamon & nutmeg. Stir in water; bring to a boil over medium heat.Boil & stir for 1 minute; reduce heat. Add apricots & butter; heat through. Pour into a greased 2 quart baking dish.
Cobbler: Combine flour, sugar, baking powder & salt in a bowl. Cut in butter until crumbly. Stir in milk just until moistened. Spoon over hot apricot mixture. Bake at 400F for 30-35 minutes or until golden brown & a toothpick inserted into the cobbler part comes out clean.