In a small bowl, mix the ground coffee with the beaten egg until the coffee grounds are well coated.
Stir in the crushed eggshell, then add in the cold water. Meanwhile, bring 8 cups of water to boil in a large saucepan.
Add coffee mixture to the boiling water and stir for about four minutes, or until the foam subsides. Remove from the heat and cover the pan.
Let stand for 7-10 minutes, until the grounds and eggshell have settled to the bottom of the pot. Strain the coffee through a wire or cloth strainer into coffee cups or into a serving carafe.
Add sugar and milk to taste if desired.