Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius).

Grease and flour a 9-inch springform pan or round cake pan.

Spread pecans on a cookie sheet.

Toast pecans in the preheated oven for 8 to 10 minutes, or until fragrant.

Remove pecans from the oven and lightly salt them.

Set the toasted pecans aside to cool.

In a large bowl, cream together the butter and sugar until light and fluffy.

Beat in the eggs one at a time, then stir in the vanilla extract.

In a separate bowl, whisk together the cinnamon, baking powder, salt, and flour.

Gradually add the dry ingredients to the wet ingredients, alternating with the sour cream, until just combined.

Do not overmix the batter.

Pour the batter into the prepared cake pan.

Peel, core, and cut the apples into 8 wedges each.

In a medium bowl, toss the apple wedges with 1 teaspoon of vanilla extract.

In another medium bowl, combine the sugar and cinnamon.

Toss the vanilla-coated apples with the sugar-cinnamon mixture.

Arrange the apple wedges in a sunburst pattern on top of the cake batter, gently pressing them in.

Bake in the preheated oven for 55 to 65 minutes, or until a cake tester inserted into the center comes out with moist crumbs.

Let the cake cool in the pan for 15 minutes on a wire rack.

Remove the cake from the pan and transfer it to a serving platter.

While the cake is baking, prepare the caramel sauce.

In a heavy-bottomed saucepan, melt the butter over medium heat.

Add the brown sugar and whisk continuously for 2 minutes, or until the sugar is melted and the mixture is boiling.

Slowly pour in the heavy cream, whisking constantly to prevent scorching.

Bring the mixture to a boil and cook for 2 minutes, or until it begins to thicken.

Remove the caramel sauce from the heat and stir in the vanilla extract.

Pour the warm caramel sauce into a large measuring cup or bowl with a pouring spout.

Let the caramel sauce cool slightly.

Before serving, drizzle the warm caramel sauce over the cake, allowing it to drip down the sides.

Sprinkle the cake with the salted pecans.