Preheat oven to 350°F; butter a 9 x 13-inch dish and set aside.
In a medium pot, combine water, milk, polenta, salt and pepper. Heat over medium heat, whisking frequently, until creamy but still very loose, about 10 minutes. Remove from heat and set aside.
While polenta cooks, heat oil in a small saute pan over medium heat. Add chopped yellow onion and cook until soft, about 5 minutes.
To the cooked polenta, add the sautéed onions, whisked eggs, 1/2 cup Parmesan, gorgonzola and green onions. Stir well to mix evenly then pour into the prepared dish.
Bake until set and a toothpick inserted in the center comes out clean, about 30-35 minutes. Sprinkle the remaining 1/2 cup Parmesan over the top and bake until cheese just begins to brown, about 5 minutes.
Remove from oven and let cool about 15 minutes before slicing.