Preheat the oven to 350 degrees.
In a large bowl, combine oil, sour cream (or yogurt), sugar, eggs and vanilla. Beat on medium speed until well combined. Scrape down the bowl once complete.
Add baking soda, cinnamon and salt. Mix until combined.
Add flour, 1 cup at a time, mixing between each addition. Once all flour has been added, beat on medium-high until well combined. Scrape down the bowl once complete.
Peel, slice and chop apples into 1-2 cm slices. Fold the chopped apples into the cake batter.
Spray the bundt pan with *baking* spray (Baker's Joy or Baking Pam Spray) or brush with oil and flour.
Gently spoon ⅓ of the batter into the pan. Place the dulce de leche in a piping bag or ziploc bag and trim a ½ inch tip. Pipe HALF of the dulce de leche around the pan, taking care to avoid the edges/center of the pan.
Gently spoon another ⅓ of the batter over the dulce de leche. Repeat step above with the remaining dulce de leche (or caramel). Gently spoon the remaining batter over the top.
Use a butter knife to gently swirl the batter around the pan (pressing all the way to the bottom and swirling). This helps distribute the dulce de leche. Only swirl 1-2 times. Do not over-swirl.
Bake the cake for 45 minutes - 1 hour or until a toothpick comes out clean.
Once baked, remove the pan from the oven and allow it to cool for 15 minutes.
After 15 minutes, flip the pan on to a wire rack to remove the cake.
Allow the cake to cool to room temperature before adding the icing.