Preheat oven to 350 degrees F. Grease a 9x13-inch pan with cooking spray and set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, 1 1/2 teaspoons cinnamon, nutmeg, ginger, and allspice. Set aside.
In a large bowl, whisk together the oil, brown sugar, sugar, eggs, and vanilla extract.
Add the dry ingredients to the wet ingredients and stir with a spatula until just combined.
In a small bowl, combine the apple chunks, lemon juice, and remaining 1/2 teaspoon cinnamon. Stir until apples are well coated.
Gently fold in the apples into the cake batter.
Pour the cake batter into the prepared pan and spread evenly with a spatula. Bake for 30 to 40 minutes or until a toothpick inserted in the center of the cake comes out clean and the cake is golden brown. Remove the cake from the oven and let it cool in the pan while you make the toffee sauce.
In a medium saucepan, add cream, butter pieces, and brown sugar. Cook over low heat, stirring, until sugar dissolves and sauce is smooth, and slightly thickened about 7 to 10 minutes. Remove from heat and stir in the vanilla extract. Let cool for 10 minutes.
Use a skewer or toothpick to poke holes over the top of the apple cake. Stir the warm sauce and pour over the cake. Spread evenly with a spatula. Let sit for 10 minutes. Cut into squares and serve.
Cover leftover cake and store at room temperature for 2 days or in the refrigerator for up to 5 days.