Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan or line it with parchment paper for easy removal.
In a large bowl, whisk together the vegetable oil and sugar until well combined.
Add the milk, vanilla extract, and dulce de leche. Mix until smooth.
In a separate bowl, sift together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix.
Add the vinegar to the batter and stir gently until incorporated. The vinegar will react with the baking soda to help the cake rise.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Remove from the oven and allow the cake to cool in the pan for 10 minutes. Then, transfer it to a wire rack to cool completely.
Once cooled, spread a layer of dulce de leche on top of the cake as frosting. You can also add a layer in the middle if desired.
Slice and serve! Enjoy your delicious egg-free Dulce de Leche Cake.