In a small saucepan over medium-high heat, combine the brown sugar, heavy cream, butter, salt, and nutmeg. Whisk until the butter melts and the mixture is smooth.

Bring to a gentle simmer and cook for 5–7 minutes, stirring frequently, until the caramel has thickened slightly and coats the back of a spoon. Remove from the heat and stir in the vanilla.

Let cool while preparing the rest of the cake. The caramel will continue to thicken as it cools.

In a small bowl, combine brown sugar, flour, cinnamon, and salt. Use clean fingertips to pinch the softened butter into the dry ingredients until thoroughly combined. Set aside. 

Preheat oven to 350°F. Grease and line a 8x8” baking pan with parchment paper.

In liquid measuring cup, measure out milk and whisk in vinegar. Set aside for 2 minutes.

In large mixing bowl, combine milk mixture, applesauce, yogurt, vegetable oil, sugars, eggs, and vanilla. Whisk until smooth. Add flour, baking soda and powder, spices, and salt. Fold dry mixture into wet until a smooth batter forms. Fold in diced apples.

Pour 1/2 of the cake batter into the prepared pan, sprinkle over cinnamon filling, spread over remaining 1/2 of the batter. Bake cake for 40-45 min until toothpick inserted comes out clean (a few moist crumbs is ok!). Allow cake to cool for 15 minutes in the pan before transferring to a wire cooling rack.

Serve cake topped with vanilla ice cream and salted caramel.