Preheat oven to 350°F (180°C). Spray a 10-inch cast-iron skillet with baking spray with flour.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter, brown sugar, granulated sugar, and vanilla at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition.

In a medium bowl, whisk together flour, cinnamon, baking powder, baking soda, and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating until almost fully combined. Fold in chopped apple and toffee. Spread dough in prepared skillet.

Bake until a wooden pick inserted in center comes out with a few moist crumbs, about 1 hour, loosely covering with foil during final 10 minutes of baking to prevent excess browning. Let cool for 5 minutes. Top with Caramel Apple Topping; serve warm with ice cream. Refrigerate in an airtight container for up to 2 days.

In a medium bowl, stir together apple, brown sugar, salt, cinnamon, and nutmeg until combined. Stir in lemon juice and vanilla.

In a medium saucepan, melt butter over medium-high heat. Cook until lightly browned, about 3 minutes. Reduce heat to medium; add apple mixture and 2 tablespoons (30 grams) water, stirring until combined. Bring to a boil.

In a small bowl, whisk together cornstarch and remaining 2 tablespoons (30 grams) water. Slowly add cornstarch mixture to apple mixture, stirring constantly. Return mixture to a boil, and cook, stirring frequently, until thickened and translucent and apples are tender, about 4 minutes. Keep warm until ready to use.