Using a whisk or an electric mixer, beat the butter with the oil and sugar until it's creamy and clearer in colour.
Add the eggs, beat them together until it's incorporated and looks thick again. If you're using a stand mixer, stop every once in a while to scrape down the sides and base of the bowl with a spatula.
Add the carrots, apples, pecans and milk and give them a quick mix. Don't worry, the batter will look split.
Add the flour, cinnamon, baking powder, salt and mix. If you're using an electric mixer make sure to mix just enough. If you do it too much, the loaf could turn out tough.
Pour the batter into a pan prepared with baking paper or greased and floured.
Bake the loaf in a preheated oven at 180°C/350°F for 45 min - 1 hour and 15 minutes. If you have an electric oven with top and bottom heat, at the 30-minute mark check if the top is already golden enough. If it is, switch to bottom heat only for the rest of the cooking process. To know if it's ready, insert a knife at the centre. It's ready when it comes out clean.
Once cold, unmould. Let it cool down completely before applying the frosting.