In a large, heavy saucepan, combine water, milk, and salt. Bring to a boil over high heat, and then reduce the heat to medium. Gradually whisk in the polenta in a slow, steady stream.
Whisk until the liquid boils again and the grains are suspended in the liquid. Keep whisking so the polenta doesn’t scorch. Once it comes to a simmer, switch to a wooden spoon and stir every few minutes until the polenta is creamy, 15 to 20 minutes. Remove from the heat and stir in the spinach, fontina, and nutmeg.
Line a table with parchment paper and pour the polenta onto the table, down the center. Top with cooked peas and parmesan cheese.