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Generously butter 13x9x1- inch baking sheet. Bring milk, broth, and bay leaf to simmer
in heavy medium saucepan. Remove saucepan from heat; cover and let steep
20 minutes to allow flavours to develop. Discard bay leaf. Bring liquid to boil.
Gradually add polenta, whisking constantly until smooth. Reduce heat to medium-low
and cook until polenta is very thick, stirring frequently, about 10 minutes.
Stir in cheese and butter. Season to taste with salt and pepper.
Transfer polenta to prepared baking sheet. Using wet hands, press polenta evenly over sheet
to edges. Chill until firm, at least 3 hours. Cut polenta out into shapes. Brush polenta with mix
of melted butter and oil. Cook on a preheated grill, 2 minutes per side, until reheated and golden.