Preheat the oven to 350°F (177°C). Grease a 9 x 13-inch pan and then dust it with flour, discarding any excess.
Peel and finely chop the apples and place them into a bowl filled with water and lemon juice. This will help prevent the apples from browning. Set aside.
Whisk the oil, applesauce, sugars, eggs, and vanilla in a large mixing bowl. Whisk thoroughly until smooth.
Mix the flour, baking powder, soda, cinnamon, and salt in a large bowl. Then, sift the dry ingredients into the wet ingredients and stir to moisten the batter. Do not overmix.
Drain the apples well and stir them into the batter, taking care not to over-stir. Pour the batter into the prepared baking pan. Bake for 45 minutes or until an inserted toothpick comes out clean. If necessary, spray a sheet of aluminum foil with cooking spray and place it over the baking cake to prevent over-browning. After cooking, use a fork to poke holes in the top of the cake.
Topping
Toast the pecans by stirring them continuously in a dry skillet on medium heat. They will burn quickly, so remove them from the pan when they start browning.
Add the butter, brown sugar, heavy cream, and salt in a saucepan and stir over medium heat. Bring to a boiling boil and then time for 2 minutes. Then, remove from the heat, and stir in the vanilla. Pour the mixture over the hot cake.
Sprinkle the chopped pecans over the topping.
Notes
Apples
Use a mix of sweet and tart apples if desired.
Caramel Topping
Reduce the cooking time of the caramel to 1 1/2 minutes to make a thin syrup to pour over the cake.
Serving Size
The serving size is approximately 180 grams (3 x 4 inches).