Combine the flour, baking powder, 1 tablespoon of the za'atar, the sugar and salt in a medium bowl using a whisk. Using a bowl scraper or your fingers, mix in the butter until the mixture resembles coarse meal; using your fingers will create a more cake-like texture. Make a well in the center and pour in the milk. Stir until just combined.
Turn the dough out onto a floured surface and knead 5 or 6 times. Roll the dough into a 1-inch-thick disc and cut out biscuits using a 3-inch biscuit cutter. Make sure you don't twist the cutter otherwise you'll squish the sides and the biscuit won't rise. Knead the scraps together, re-roll and cut out biscuits until all the dough has been used.
Place the biscuits bottom-side up on a baking sheet lined with parchment paper. Whisk together the vegetable oil with the remaining 1 tablespoon za'atar and brush the mixture on each biscuit. Bake until golden brown, 18 to 20 minutes.