1. Melt butter in a large nonreactive skillet over medium-high heat. Add pineapple, brown sugar and ginger and cook, stirring, until sugar has dissolved and pineapple begins to brown, 3 to 4 minutes. Transfer to a bowl and let cool slightly. Stir in lime juice.
2. Divide ice cream among 4 bowls and spoon pineapple mixture on top. Serve immediately.