Preheat the oven to 180°C using top and bottom heat (no fan).
Beat the room-temperature eggs with the sugar for about 7 minutes until light and fluffy.
Gently warm the milk together with the butter until the butter melts completely—be careful not to let it boil.
In a separate bowl, combine all the dry ingredients.
Gradually add the dry ingredients to the egg-sugar mixture in three parts. Mix just until incorporated—avoid overmixing.
Pour in the warm milk and butter mixture, then mix until smooth. Add the oil and mix again briefly.
Place a piece of chocolate in each muffin cup, then fill each one 2/3 full with the batter.
Bake the muffins in the center of the oven for 12–14 minutes.
If using a metal tin, remove the muffins from it about 2 minutes after taking them out of the oven.
Dust the tops of the muffins with icing sugar before serving.