Place a thigh onto a cutting board. Using a sharp sturdy knife place the blade onto the leg bone about 3/4 of an inch from the ankle. What you are looking for is the soft spot. It is a spot where, when pressure is applied with your free hand to the back of the knife, the blade will slip through cartlidge instead of pure hard bone. If you miss and hit bone it is ok it is just harder to cut and sometimes the bone splinters a little.
With the blade resting on the bone grip the knife handle firmly. Place the lines palm of your free hand onto the spine of the knife keeping your hand flat as if you were pushing on the counter itself. In other words you are keeping you fingers well out of the way in case the knife tips. Apply a good amount of pressure and push the knife through the bone. Repeat this with all four thighs.
Place the not yet protruding bone between you forefinger and index finger like you are making the peace sign. Put your thumb on the knee of the chicken and then scrunch the peace sign down pulling the meat with it. It may take some practice to get the feel of this technique but once you do it is easy.
Season the chicken on all sides with salt and sprinkle on the za'atar dividing it evenly between all four pieces. Sprinkle some of the garlic onto the bottom of a snug fitting casserole. If it is snug you will use less buttermilk.
Place the chicken on top of the garlic then top the chicken with the remaining garlic. Pour buttermilk over the top of the chicken until it is three quarters covered. Top with the thyme.
Place the chicken into the fridge for at least 10 but no more then 24 hours.
A half to one hour before baking remove the chicken from the fridge to get it closer to room temperature.
Place the chicken into a heated 375?F oven. and bake for 20 minutes. Turn the oven to 450? F and bake another 15 to 20 minutes making sure the top of the chicken is nice and caramelized.
Remove from the oven and serve using the broth as a sauce and don't let the curdled buttermilk cheesy stuff go to waste either. Serve.