Combine the milk, 1/2 cup water, the cayenne and bay leaf in a medium saucepan. Bring to a boil and season generously with salt. You want to take the seasoning to the edge of too salty in this case; to do this you MUST taste as you go! Polenta acts like a "salt eraser"; if you don't salt abundantly in this early step, you'll never recover.
When the liquid comes to a boil, gradually sprinkle in the polenta, whisking constantly. Once the polenta is combined, IMMEDIATELY switch over to a wooden spoon and stir frequently until the polenta thickens, 30 to 35 minutes. Taste the polenta to see if it's cooked through. If it still feels mealy and grainy, add some more milk or water and continue to cook for another 10 minutes. Repeat this process as needed until the polenta feels smooth on your tongue. Remove the bay leaf and stir in the mascarpone and Parmigiano-Reggiano, then remove from the heat.
Line a 7-inch square baking pan with plastic wrap. Pour the polenta into the pan and cover with plastic, pressing down so the plastic sits on the surface of the polenta. Chill until set, at least 45 minutes. (All of this can totally be done ahead of time, like yesterday!)
Preheat the oven to 400 degrees F.
Cut the cooled polenta into 1-inch squares. Place the squares on a baking sheet and top each with a piece of taleggio. Put the cherry tomatoes on a separate baking sheet and toss them with olive oil. Bake both the polenta squares and the tomatoes for 10 minutes. The tomatoes should be hot, starting to relax and getting a little squishy, and the taleggio should be nicely melted. Place the polenta cakes on a serving dish, top each square with a tomato half, and garnish each with a little sprinkey-dink of coarse sea salt and chives.