Place tulip-shaped cupcake liners in the cups of a 12-muffin tin; set aside.
In a large bowl, sift together the almond flour, baking powder, and salt.
In a separate bowl, whisk together the olive oil, 1/4 cup sugar, orange zest and juice, egg yolks, and vanilla.
Fold in the flour mixture.
In a very large bowl or the bowl of a stand mixer, beat the egg whites on a low speed to break them up, about a minute.
Once they start to foam, increase the speed to high and add the remaining sugar.
Whip until the whites form stiff peaks, then use a large spatula to gently fold them into the almond flour mixture in 3 or 4 batches, rotating your mixing bowl as you move your spatula from the center out to the sides.
Don’t overmix to avoid deflating the batter—a few streaks of whites are OK.
Use a large ice cream scoop to fill the paper liners up to the level of your baking tin.
Top with equal amounts of berries.
Bake the muffins for 30 to 40 minutes, until the tip of a sharp knife comes out clean.