apple cake with apple cider soak, brown butter crumble, and cinnamon frosting

Ingredients

• 2 cups diced apples heaping (about 2 medium apples)
• 1 tablespoon light brown sugar
• 1 teaspoon ground cinnamon
• 2 cups flour
• 2 teaspoons baking powder
• ¾ teaspoons salt
• 1 ½ teaspoons ground cinnamon
• ¾ teaspoons ground nutmeg
• 1 cup vegetable oil
• ½ cup light brown sugar, packed
• 1 cup granulated sugar
• 3 large eggs room temperature
• 1 teaspoon vanilla
• ¼ cup apple cider
• 1 teaspoon light brown sugar, packed
• pinch of ground cinnamon
• 1 ½ cups flour
• ¼ teaspoon ground allspice
• ¼ teaspoon salt
• ¾ cup light brown sugar, packed
• ¾ cup butter (1 ¼ sticks), browned (see how-to in this recipe )
• 1 ½ cups (3 sticks) unsalted butter, room temperature
• 5 cups powdered sugar, sifted
• 2 teaspoons vanilla
• pinch of salt