Apple Cake with Rum Sauce

Name: Apple Cake with Rum Sauce
Ingredients: For the apple cake:; 1 cup all-purpose flour; 1 teaspoon baking soda; 1/2 teaspoon salt; 1 teaspoon cinnamon; 1 teaspoon freshly grated nutmeg; 8 tablespoons unsalted butter, room temperature; 1 cup sugar; 1 egg; 1 teaspoon vanilla; 1/8 cup water; 1/2 cup toasted pecans or walnuts, chopped; 2 1/2 cups Granny Smith apples (about 3), peeled, cored, and diced into small pieces; For the rum sauce:; 1/4 cup heavy cream; 3/4 cup brown sugar; 8 tablespoons unsalted butter; 1 tablespoon rum; a good pinch of salt