Bring the milk and water to a low boil over medium heat in a medium saucepan. Add the oats, return to a simmer, reduce the heat to medium-low and cook, stirring, until the oats are tender and have absorbed most of the milk, 7–8 minutes. Stir in the Parm, mozzarella, salt, and pepper and cook until the cheese is melted, 1 minute. Remove from the heat, divide among bowls (or leave in the saucepan), and garnish with more Parm and pepper.