Preheat oven to 375°. In a large ovenproof skillet over medium heat, melt butter and cook until lightly browned and fragrant, about 4 minutes. Stir in brown sugar and wine. Raise heat to a simmer and add rhubarb, stirring well to coat.
Place pan in oven 4 minutes. Remove (remember, the handle will be hot) and stir gently. Try not to break up rhubarb. Cook in oven 2-5 more minutes longer, depending on the rhubarb's thickness; it should be just tender but not falling apart. Set aside and let cool (or refrigerate up to 4 days).
In a clean, dry bowl, whip cream until it begins to thicken. Add sugar and whip to soft peaks. In parfait glasses, layer rhubarb, diced mango, ice cream, and whipped cream; repeat until filled. Top with nuts.