Preheat oven to 180C and grease a 12-hole nonstick muffin tray well with oil. Pour the melted butter into large mixing bowl. Add the egg, sugars, and vanilla and mix to combine until smooth. Add the flour and baking powder and stir until just incorporated. Fold in the chocolate chips.
Distribute the dough equally between the 12 muffin tray cavities; each will approximately be filled to between two-thirds and three-quarters full.
Bake for 10 minutes, or just until tops have set and are golden; allow muffins to cool in the tray for at least 20 minutes before removing them.