Preheat oven to 350°F. Generously grease a round 9-inch baking pan.
In a small saucepan over medium heat, melt butter and brown sugar together for 2-3 minutes, stirring until smooth. Pour into prepared baking pan.
Arrange apple slices on top of caramel so that they’re slightly overlapping each other.
In a small bowl, combine flour, baking powder, salt and cinnamon. Set aside.
With an electric mixer, beat butter and sugar on medium high speed until pale and creamy, about 3 minutes.
Add the eggs one at a time, mixing after each. Mix in vanilla.
Add flour mixture in 3 additions, alternating with the milk, and ending with the flour mixture. Mix until just combined.
Pour batter over apple slices and gently spread it into an even layer.
Bake cake until top is golden brown and center springs back when gently pressed, about 45-55 minutes.
Let cake stand about 10 minutes. While cake is still warm, run a knife around the edges and invert it onto a plate or cake stand. If you wait till cake is cool, it may not come cleanly out of the pan.
To make the caramel sauce, add the brown sugar, butter, and milk in a saucepan over medium heat. Bring to a boil and simmer for 3-4 minutes, stirring often, until caramel is smooth and thickened. Remove from heat and stir in vanilla extract and salt.
If desired, top cake slices with additional caramel sauce before serving.