Grease and flour a tube pan.Preheat oven to 350°.In a large mixing bowl, stir together sugar, self-rising flour and cinnamon until combined.Stir in beaten eggs, cooking oil and vanilla.Stir in diced apples (and optional nuts) until just combined.(Batter will be very thick, maybe even crumbly.)Spoon batter into prepared pan.Bake for 50 - 60 minutes. (Check with cake tester at the 50 minute mark.)Remove from oven and let cool on a rack 20-30 minutes until warm.Loosen all edges including around the center tube with a sharp knife before turning out onto a cake platter.In a medium-sized sauce pan stir together 1/4 cup cold water and granulated sugar until combined.Set over medium-high heat on the stove top and cook 9 -11 minutes without stirring until mixture is a deep amber color.Start checking closely at the 8 minute mark.Meanwhile, warm heavy cream and butter together with sea salt in a small sauce pan over medium heat. (Absolutely do not boil.)When sugar and water mixture is a deep amber color, slowly whisk in the warm cream and butter mixture.Whisk over the heat until it's smooth a minute or two, then remove from the heat.Salted caramel sauce will thicken up as it cools.When sauce is still warm, spoon over apple cake and cascade down the sides.(Re-heating the caramel sauce will thin it.)