In a large bowl whisk together the flour, baking soda, ground ginger and salt.
Heat the butter in a small saucepan until just barely melted. Stir in the molasses, dark muscovado sugar. The mixture should be warm, but not hot. If it is hot to the touch, let it cool until just warm. Once cool whisk in the egg. Pour this mixture over the flour mixture and add the chopped apricots and chocolate and then stir until just combined. Chill the dough for about 30 minutes, until the dough has firmed up a bit.
Pour some of the demerara sugar into a bowl. Use a tablespoon to scoop the dough, split that tablespoon into two smaller pieces, and roll each into a ball. Roll each ball in the bowl of demeara sugar, using pressure if needed to make the sugar stick to the dough.
Place the cookies on the baking sheets a few inches a part. Bake for about 7 – 10 minutes until the cookies puff up, darken a bit and crack. Cool on a wire wrack.