Mix the starter. Warm milk in microwave for 30 seconds. Combine milk, flour, yeast, and sugar in a bowl. Stir until dissolved. Let stand for 10 minutes until light foam appears and small bubbles are visible. Proofing is done to test yeast viability. If there is no foam or bubbles, discard and use new yeast.
Mix the dough. Add remaining flour, water, olive oil, and salt to the starter. Mix until no dry flour remains and a cohesive mass forms. Cover and let rest for 30 minutes.
Bulk Fermentation + Gluten Development. Perform a stretch and fold by grabbing a corner of the dough, lift straight up to stretch the dough as high as it will go without tearing and fold over to the other side. Rotate the bowl and perform three more reps of stretch and folds. Once folded, turn the dough over onto itself, cover and let rest another 25-30 minutes.
Proofing (Second Ferment). Oil or place parchment paper on a circular pizza pan or rectangle baking sheet. Turn the pide dough into the pan and gently work it into a circle. If the dough is springing back from the edges, cover and let rest for 15-20 minutes before gently working to the edges. Cover the pan and let the pide proof for another 30 minutes. Preheat the oven to 450 F.
Egg Wash, Dimple + Add Seeds. Dimple the proofed dough with wet fingers by gently pushing to the bottom of the pan, but do not accidentally go through the dough. Whisk the egg yolk and water together with a fork until it emulsifies, about 2-3 minutes. Brush over the pide. Sprinkle over the nigella seeds.
Bake. Place on middle rack of the 450 F oven and bake for 20-25 minutes until golden on top. Let rest under a cloth on a wire rack for 5 minutes before slicing into large triangles for doner.
For Doner Sandwiches. Place a triangle in a wet paper towel. Microwave for 30 seconds. Toast in a pan and flatten with a press or another pan before assembling.