Combine chopped dried apricots, orange juice, ?½ cup water and chopped fresh ginger in heavy medium saucepan. Cover tightly and simmer until liquid is reduced by half and apricots are very tender, stirring frequently, about 20 minutes. Puree apricot mixture in processor until smooth. Mix in 2 tablespoons honey and 2 tablespoons sugar. Season butter to taste with more sugar, if desired. Transfer butter to bowl and cool completely. (Butter can be made 1 weeks ahead. Cover tightly and refrigerate.)