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Preheat oven to 350 degrees F. Line a 12-cup muffin tin with paper liners.
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In a small bowl, whisk to combine flours, baking powder and soda, spices, and sea salt. In a large bowl or the bowl of a stand mixer fitted with the paddle attachment, beat eggs and brown sugar on low for 4 minutes or until pale and frothy. Fold in vanilla and apple. With mixer on low, add half the flour, the olive oil, and remaining flour. Switch off mixer and stir by hand just until all the flour is folded in.
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Spoon into prepared muffin tin. Top muffins with a sprinkle of sugar and a few flecks sea salt, if desired.
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Bake until muffins are golden brown, springy to the touch, and a toothpick inserted in the middle comes out with just a few crumbs attached, 25 - 35 minutes. Cool briefly, then serve (preferably slathered with salted butter).
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Muffins will keep in an airtight container at room temperature for 3 days.