In a large saucepan, steam the squash until barely tender, about 7 minutes. Let cool slightly and pat dry. In a large nonstick skillet, melt the butter with 1/4 cup of the sugar. Add the squash and cook over moderately high heat, stirring occasionally, until golden, about 12 minutes. Add the ginger and cook, stirring, for 1 minute. Transfer two-thirds of the candied squash to a food processor and puree until smooth.