In a medium pot, whisk the eggs, brown sugar, ginger, and lime juice together.Stir in the coconut milk until combined.Heat over a medium flame, stirring continuously, until thickened. The mixture should coat the back of a spoon.Strain into a heat safe bowl and chill until completely cooled.Churn the custard in an ice cream maker, according to the manufacturer's directions.Layer the semi-frozen ice cream (in a freezer safe container), alternating with grilled pineapple, and freeze solid.Sandwich a scoop of ice cream between two peanut butter cookies, and serve.