In a heavy-bottomed 4-quart saucepan, heat milk, stirring frequently, over medium heat to 185 degrees. Remove from heat and let cool to 110 degrees.
Place the yogurt in a medium bowl. Using a whisk, gradually stir in the cooled milk, about 1/2 cup at a time, stirring until smooth between additions. Cover the bowl with plastic wrap, poking 2 or 3 holes for ventilation. Transfer to a warm place (about 90 degrees) until the milk begins to thicken around the edges and the yogurt is set, about 5 hours.
Place bowl in refrigerator until completely chilled. Reserve at least 1/4 cup of this yogurt to begin next batch. Refrigerate up to 2 weeks in an airtight container.