Scald the 3 pints of milk in the top of a double boiler over hot water.
Melt the chocolate and ¼ cup milk over low heat. To this mixture add the scalded milk, beating gently to blend well.
Beat the egg yolks, 1 cup sugar and vanilla together until frothy and lemon-colored. Add the chocolate mixture in small quantities, beating gently but thoroughly.
Return to the top of the double boiler and let stand over the hot water, heat turned off, until it thickens.
Whip the egg whites stiff with the 6 tablespoons of sugar.
To serve, place the mixture in bowls and top generously with the egg-white mixture.