Thoroughly soak the towel and then wring out excess water — you want it to be moist, not wet. Lay it out on the oven rack directly and then place your eggs on it. Then, just like in the oven-bake recipe, you need to bake at 160 degrees C for 30 minutes.
The moist towel has two advantages. First, it stops the eggs from coming into direct contact with the wire rack so there’s no discolouration and they get a bit of insulation from the direct heat. Second, once the eggs are done, the towel won’t be too hot so you can just wrap them all and pick them up, without the risk of breaking them.
Alton Brown’s Oven Eggs [Alton Brown]