CUT squash into quarters. Scoop out and discard seeds. Roast pieces in a large baking dish covered with foil, until fork-tender, about 1 hour. Remove from oven. (Reserve pieces for garnish, if desired.) When cool enough to handle, scoop flesh from skins. Whirl in a food processor until smooth. (Refrigerates for up to 3 days.)
COMBINE milk with water, 1 cup of acorn squash purée, cornmeal and salt in a large saucepan over medium-low. Cook, whisking often, until polenta is tender and slightly thickened, 12 to 15 min. (Mixture may splatter.) Stir in butter until combined. Top with roasted acorn squash pieces, if desired.