Combine the sugars and cream in the top part of a double boiler and cook over simmering water, stirring occasionally, for 1 1/2 hours. Add the butter and cook another 30 minutes. (The mixture may look curdled but will smooth out when beaten). Remove from heat, add the rum and beat until smooth.
PREPARE THE CAKE:
Preheat the oven to 350°F. Spray a 10-inch pie plate or 9-inch square baking pan with nonstick spray. Use an electric mixer to combine the butter and sugar until light and fluffy; beat in the eggs and vanilla until well mixed. Whisk together the flour, cinnamon, nutmeg, soda and salt; blend into the butter mixture. Stir in the apples and pecans (if using). Spoon the the batter evenly into the prepared pan and bake about 45 minutes or until golden brown. Serve topped with the warm sauce.
Notes
The best apples for baking are Jonagold, Honeycrisp, Braeburn and Pink Lady.
Nutritional information does not include the (optional) pecans. Numbers include using ALL of the caramel sauce when serving. You're likely not going to use all of it, so the numbers will very likely be lower.