Preheat oven to 300 degrees F (150 degrees C). Grease a 9x13-inch baking pan.
Combine white sugar, oil, and eggs in a large bowl; beat with an electric mixer until smooth. Add apples, flour, 1 teaspoon vanilla extract, and cinnamon; beat until a thick batter forms. Spread batter in the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 70 minutes. Poke holes in the hot cake with a fork.
Combine brown sugar, butter, heavy cream, and 1 teaspoon vanilla extract in a small saucepan over medium heat. Bring to a boil; cook for 2 1/2 minutes. Pour immediately over the warm cake. Let cake sit for 3 hours to soak up the glaze.