In a bowl, combine the sliced almonds, orange zest, egg whites and confectioner's sugar and gently mix to combine.
Preheat oven to 300 degrees F. Line 2 baking sheets with parchment paper brush with a little vegetable oil. Take about 1/4 cup of the almond mixture and place on the prepared baking sheets. Using your hand or the back of a fork dipped in the water, gently flatten almond cookies. The cookies should be as thin as possible without having gaps between the nuts.
Bake for about 18-22 minutes, or until the florentines are golden brown all over (cooking time depends on the size of the cookies). Remove from the oven and allow to cool completely on the baking sheets before removing.