Preheat oven to 375 ° F. Line a 12-cup muffin tin with liners.
In a large bowl, whisk together the olive oil, egg, coconut sugar, and coconut buttermilk, mixing well to combine. In a medium bowl, whisk together the dry ingredients until combined. Pour the dry ingredients into the wet mixture and stir and whisk until combined. Gently fold in the chopped apples and nuts if using.
Portion out the batter equally between the muffin cups. Let the batter rest while the oven finishes preheating.
Place the muffins in the oven and bake for about 25 minutes, until a tester inserted in the middle comes out clean, the tops are slightly firm, and the edges are starting to come away from the sides of the liner.
Remove from oven and gently place the muffins on a wire rack to cool completely. They will firm up as they cool. Serve at room temperature or from the fridge.
Muffins will keep in an airtight container for up to 5 days in the refrigerator.