In a saucepan combine the milk, water, bay and cayenne. Bring the mixture to a boil over low heat and season generously with salt. Take the seasoning to the edge of too salty. To do this you MUST taste as you go. Polenta acts as a salt eraser, if you don't season abundantly here you will never recover from it.
Once the liquid is at a boil and is seasoned appropriately, sprinkle in the polenta whisking constantly. Once the polenta is combined switch over to a wooden spoon and stir frequently until the polenta has become thick. Taste the polenta to see if it has cooked through. If it still feels mealy and grainy, add some more milk or water and cook it to a thick consistency. Repeat this process, as needed, until the polenta feels smooth on your tongue, about 30 minutes. Remove the bay leaf and stir in the chopped sage and mascarpone.
Line a 7 by 7-inch square pan with plastic wrap. Pour the polenta into the prepared pan. Cover the top with more plastic smoothed onto the surface of the polenta. Chill in the refrigerator until needed. (All of this can totally be done ahead of time, like yesterday! Cool!)
When ready to use, remove the polenta from the pan and cut into desired shapes. Coat a nonstick saute pan with olive oil and bring to medium-high heat. Once the pan is hot and starting to smoke just a little, add the polenta shapes. Cook the polenta on both sides and finish by sprinkling with a little bit grated Parmigiano. Transfer to a serving platter and serve while hot.