Preheat oven to 350ºF. Line one 12 cup muffin tin and one 6 cup muffin tin with paper liners; set aside. Whisk flour, cocoa, baking powder and salt in a bowl; set aside.
In a separate bowl, whisk eggs, sugar and olive oil, until thick and well-mixed.
Whisk in the vanilla extract.
Add the flour mixture and pour in the milk, stirring well with a wooden spoon until combined.
Spoon batter into prepared muffin cups, filling 2/3 of the way.
Bake for 18 to 20 minutes, until center springs back when gently touched or a metal skewer inserted, comes out clean.