For the polenta: Combine the cream, milk and salt in a medium saucepan. Turn the heat to medium-low and slowly bring to a boil, making sure to whisk often so that the milk doesn't scorch. Slowly whisk in the polenta, making sure to whisk out any lumps. Turn the temperature to low and cook, stirring every few minutes, until the mixture is smooth and silky, 45 minutes to 1 hour. Remove from the heat and whisk in the cheese and butter.
For the mushrooms: Preheat the oven to 400 degrees F.
Spread out the mushrooms on a sheet pan. Drizzle with olive oil to lightly coat. Toss and spread out in an even layer. Roast until browned around the edges, about 25 minutes.
Meanwhile, add the bacon lardons to a large saute pan. Turn the heat to medium and cook until the bacon is crisp, about 10 minutes. Remove the bacon to a paper towel-lined plate.
Add olive oil to the pan if needed to lightly coat. Add the shallots and saute until translucent, about 3 minutes. Add the mushrooms and toss to combine until starting to brown. Add the veal demi-glace or stock to deglaze the pan (if using demi, add 1/2 cup water and stir to combine). Add the thyme and stir, then reduce by three-quarters, about 10 minutes. Add the bacon and mix to combine. Taste and season with salt as needed.
Add the polenta to a wide shallow bowl or platter and add the mushrooms to the center. Garnish with chives, shaved Parmesan and truffles, if using. Serve!