Preheat the oven to 350 °F. Line a 9" x 13" baking pan with a piece of parchment paper or alternatively spray the pan with baking spray.
In a medium mixing bowl, stir together the flour, 1 tablespoon cinnamon (ignore the quantity below - it's a technical issue I can't fix), nutmeg, baking soda, and salt. Set aside.
1 3/4 cups (219 grams) flour, 1 tablespoon + 1 teaspoon ground cinnamon, 1/2 teaspoon ground nutmeg, 1 teaspoon baking soda, 1/2 teaspoon salt
In a large mixing bowl, stir together the brown sugar, granulated sugar (ignore the quantity below - it's a technical issue I can't fix), oil, eggs and vanilla until thoroughly combined. Add in the flour mixture and mix just until well combined.
1 cup (200 grams) brown sugar, 3/4 cup (150 grams) granulated sugar, 1 cup (225 grams) oil, 3 large eggs, 2 teaspoons vanilla extract
Place the apples in a small bowl and sprinkle the remaining 1 tablespoon granulated sugar and 1 teaspoon ground cinnamon over the apples. Stir to coat the apples in the cinnamon sugar. Fold the apples into the batter.
3 1/3 cups (367 grams) peeled and diced apples, 1 tablespoon raw sugar
Pour the batter into the prepared pan and bake for 33-40 minutes or until a toothpick inserted in the center comes out clean. Let cool completely before frosting, about 1 hour.
Prepare the frosting. Melt the butter in a medium saucepan over medium heat. Stir in the brown sugar and whipping cream. Once the mixture starts bubbling, stop stirring. Let the mixture come to a full boil and boil for 1 minute without stirring. Remove the pan from the heat. Stir in the vanilla, 1/4 teaspoon salt, and gradually add the powdered sugar. Whisk until the powdered sugar is fully incorporated and no lumps of sugar remain. Add the remaining 1/4 teaspoon salt, if desired. Once the cake has cooled, spread the frosting over the top and refrigerate any leftovers for up to 4 days. Let come to room temperature before serving.
1/2 cup (113 grams) unsalted butter, 1 cup (200 grams) brown sugar, 2/3 cup (158 ml) heavy cream, 2 teaspoons vanilla extract, 1/4-1/2 teaspoon salt, 1 1/2 cups (165 grams) powdered sugar