Banana Pudding with Salted Caramel Sauce

Sprinkle the sugar in an even layer in a medium heavy-bottomed saucepan set over medium-high heat. Using a heatproof rubber spatula, stir the sugar until it begins to melt and darken in color, about 10 minutes. (If chunks form, continue stirring until they dissolve.) Stop stirring and let the sugar cook, undisturbed, until it turns amber in color, about 5 minutes. Remove the melted sugar from the heat and whisk in the butter until combined, then slowly and carefully whisk in the heavy cream. (It will bubble vigorously.) Stir in the sea salt then transfer the caramel to a glass container to cool while you prepare the pudding.