Stir in the wine and chicken stock. Gently press the chicken pieces down into the mushrooms, and add the thyme sprigs. Reduce heat to just shy of medium and let simmer until liquid is reduced and chicken is cooked through, about 20 or 25 minutes.
Meanwhile, make the creamy polenta. Heat the stock, water, & milk to a low simmer in a medium saucepan. Generously season with salt and pepper. Gradually whisk in the cornmeal making sure there are no lumps. Stir regularly until the polenta is very thick and creamy, about 20 minutes. Remove from heat and stir in grated cheese. Taste and adjust seasoning if necessary.
Once chicken is cooked through, remove thyme sprigs. Spoon polenta into a bowl and top with mushroom mixture and some reduced liquid. Top with a piece (or two if small) of chicken.
Recipe by Honest Cooking at https://honestcooking.com/braised-chicken-thighs-mushrooms-creamy-polenta/