In a saucepan, over medium heat, melt the butter. Add the ginger and cook, stirring, for 2 minutes. Stir in the cranberries, sugar, orange juice, and preserves. Cook, stirring occasionally, until the cranberries burst and the sauce thickens, about 20 minutes. Transfer to a bowl and serve warm.
While the cranberries cook, seed and finely chop 1 jalapeño.
Remove the sauce from heat. Stir in the jalapeño and cilantro. Serve warm or at room temperature.
Make-Ahead Note: The sauce can be made up to 2 days in advance.