Fold the paper towel to fit into the 1 Quart Saucepan.
Wet the paper towel with water and place in the pot. (The towel shouldn’t be sitting in a pool of water. All the water should be held in the towel.)
Place the eggs in a single layer on top of the wet towel.
Cover the pot and heat over medium heat until steam just begins to escape from under the lid, about 3 minutes.
Spin the lid to engage the vapor seal then immediately reduce the heat to low.
Cook 5 to 6 minutes for soft-cooked eggs; cook 7 to 8 minutes for medium cooked eggs; cook 13 to 15 minutes for hard-cooked eggs.