In the bowl of a stand mixer, combine the warm water (105-115°F or 40-46°C) and honey until it dissolves. Then, add in the active dry yeast and let everything rest for 10-15 minutes. If your yeast is live, the mixture will bloom.
While that sits, measure out the flour and set aside. Then, mix the oil, egg, salt, and labneh in another bowl.
Once the yeast has bloomed, turn on the mixer (with the whisk or beater attachment on) and add in the egg mixture. When incorporated, add in flour a little at a time until it's about the viscosity of pancake batter or the machine starts to slow from mixing the dough.
Switch out the beater attachment for a dough hook and continue mixing until the dough fully incorporates and cleanly pulls away from the sides of the bowl. The dough will also change from matte to slightly shiney (maybe 5-7 minutes). Don't overmix. The dough will not pass a windowpane test yet (see FAQs) and will still appear mottled when stretched. Cover the bowl and let the dough rest for 10-15 minutes.
Next, hold onto the bowl with one hand and with the other hand take your fingers and quickly pull the bottom of the dough up and over towards the middle of the ball turning the bowl in a circle as you go for about 1 minute. (If needed, use wet or oiled fingers to help keep the dough from sticking to your fingers.) The faster you go the less the dough will stick.
Rest and repeat (every 10-15 minutes) 2-3 more times. The dough will get stretchier, shinier and smoother but will probably still not pass the windowpane test (FAQs again) with flying colors (this is okay). You should be able to feel that the dough has relaxed and softened to the touch. Additionally, by the 3rd or 4th turn, you should be able to tap and manipulate the dough a few times without it sticking to your fingers. If not, either let it rest for one more turn or add in a small amount of flour to the dough to lessen the hydration a bit. (See notes)
Dump out the dough on your counter and shape into a ball. Then, place in into a bowl that's been lightly coated in oil. Cover it with plastic wrap (cling film) or a damp towel. Set the bowl aside for 60-90 minutes for the dough to double in size.
Once the dough has doubled, gently place it into the refrigerator for at least 6 hours and up to 12 hours for cold proofing. For naan or pita pockets (about an hour before you are ready to take the dough out of the refrigerator) place a pizza stone or steel onto your top oven rack and turn on your oven as high as it can go. This is typically between 500-550°F (260-288°C).
Now, retrieve your cold-proofed dough and scrape it out of the bowl onto a well-floured countertop. Coat the dough just enough that you can place it onto a kitchen scale. Weigh the dough for a total weight and divide by the number of flatbreads you’d like. (12 equal pieces should be ≈ 75-80g per piece.) Shape the pieces of dough into small balls by pulling the bottom of the dough up and over towards the middle of the ball from all four corners. Then rotate it 45 degrees and fold from the bottom again. Turn the whole thing over making sure the folds stay tucked. Then, gently rotate and shape the dough finalizing your sphere.
Set your dough balls on a silicone mat lined baking sheet under a cloth or more plastic wrap and rest between 15 and 45 minutes. If you are making naan, prep melted butter or ghee, salt, and other toppings (see notes) now.