Combine milk, 5 tablespoons butter, salt, pepper and nutmeg in heavy large saucepan. Bring to boil over medium heat. Gradually whisked in cornmeal. Stir until mixture is very thick and beginning to pull away from sides of pan, about 8 minutes. Remove from heat. Mix in ham, 3/4 cup cheese and egg. Transfer polenta to 8 x 8 x 2-inch glass baking dish. Dot with 1 tablespoon butter. Sprinkle with remaining 2 tablespoons cheese. (Can be prepared 1 day ahead. Cover; refrigerate.) Preheat oven to 450°F. Bake polenta uncovered until heated through and beginning to brown on top, about 30 minutes. Cut into squares and serve.