Preheat oven to 375°F and grease 12 muffin cups or line with muffin liners.
In a large bowl combine flour, baking powder, salt and baking soda. In a small bowl, mix egg, buttermilk and olive oil with a whisk until evenly combined. Stir wet ingredients into dry ingredients and mix in feta, peppers and basil.
Fill muffin cups ¾ of the way full with the batter and bake for 18-20 minutes or until a toothpick inserted into the middle of a muffin comes out clean. Cool before removing from the tins.