Line 12 to 14 muffin cups with paper liners. Preheat oven to 350° F.
Sift the flour, arrowroot starch, baking powder and salt into a large bowl.
In another bowl, whisk the oil, honey, egg yolks, lemon zest, lemon juice, water, and vanilla.
Add to the flour mixture and whisk until smooth.
In a large bowl of a heavy duty mixer fitted with the whisk attachment, whip the whites on medium speed until foamy. Add the cream of tartar and continue whipping until the whites form soft peaks. To prevent overwhipping, remove from the mixer and finish whipping by hand. Resist the urge to whip just a little more--you don't want the beaten egg whites to get stiff and dry.
Stir about 1/3 of the whipped whites into the batter to lighten it. Gently fold in the remaining whites. Divide into lined muffin tins.
Bake until the cupcakes are light golden and the tops spring back when gently pressed with a finger, 15-20 minutes. Cool.
Cut a small hole out of the top of each cupcake and remove a piece of the cake. Fill the hole with lemon curd.