In a large saucepan, combine the water, milk and salt and bring to a boil. Whisk in the grits and simmer over moderate heat, stirring constantly, until thickened, about 8 minutes. (For thinner grits, add an extra 1/2 cup water.) Remove from the heat and stir in the Fontina and Parmigiano-Reggiano. Season with salt and pepper.
Fill a deep, medium skillet with water and bring to a simmer. Add the vinegar. Crack the eggs into individual cups or ramekins, then carefully slide them into the water. Poach the eggs until the whites are set but the yolks are still runny, about 3 minutes. Drain the eggs and gently pat them dry.
Spoon the grits into bowls and top each serving with the chopped watercress. Set the eggs on the watercress and serve immediately.