Mix the egg into the coffee grounds, breaking the shell. Add 1 cup of cold water and mix. Tie this mixture in cheesecloth with room for the coffee grounds to swell.
Pour the 9 quarts of cold water into a large pot. Immerse the package of coffee grounds in the water. Bring to a boil.
Remove the pot from heat . Leave package of coffee grounds to steep in the water for 3-4 minutes. Remove and stir. Be sure to keep coffee hot.