Whip up the butter with the sugar, salt and oil until the mix becomes lighter. You can do this with an electric mixer or using a hand-held whisk.
Add the eggs and beat them again until they are fully incorporated and the mix looks airy. From all the whipping, the mix should thicken and start to unstick from the sides of the bowl.
Add the milk and vanilla extract and mix. It will look split, but don't worry. It will come back with the flour.
Add the flour and baking powder and mix, then add the chips and fold them in.
Grease your bundt pan with a thin layer of melted butter using a pastry brush. Flour the pan. After distributing the flour around the inside of the pan, turn it upside down and pat it to remove the excess.
Place the batter inside the pan and spread it out. With a spatula, bring the batter up the sides so that when it rises in the oven it evens out.
Bake the cake at 180°C/350°F for 40min-45min or until a knife comes out clean. It's important to not overcook it to prevent it from drying out. If you have an electric oven, check the cake at the 30-minute mark. If it's golden enough on top, change the heat source to only the bottom.
Unmould the cake while it's still hot.