Preheat oven to 180°c (356f).
In a medium sized bowl cream butter with sugar. Then mix in eggs (preferably one at a time with mixing).
Whisk in yoghurt, lemon zest, and vanilla. Give the mixture a good mix.
Add flour, baking powder, and salt. Mix again but do not over mix at this point.
Pour the batter into the greased muffin pan and bake for 20 to 25 minutes or until a toothpick comes out clean.