Bring milk, 2 cups (500 mL) water and salt to a boil in a large saucepan. Slowly whisk in cornmeal. Continue whisking until cornmeal thickens, about 1 min. (Work quickly and have the saucepan lid close by, as polenta can boil quite vigorously.) Reduce heat to low and cook, covered, stirring every 5 min., until polenta is very thick and no longer gritty, about 30 min.
Remove from heat and stir in cheese, rosemary and butter, until cheese has melted, about 2 min.
The polenta will solidify once it cools. Spread the warm polenta in a greased 8-in. (20-cm) square dish or onto a wooden board and slice into squares once cooled. Grill polenta squares to reheat.