In a saucepan, melt the duck fat. Add the mushrooms and cook until they are golden. Season with salt and pepper. Add the parsley. Keep the mushroom mixture warm.
In a sauce pot, combine the chicken broth and the cornmeal with a whisk. Season with salt and pepper. Over low heat, cook the mixture just until it thickens and comes together, like a pate a choux. Add the mascarpone and the cheese. Stir until melted. Adjust seasoning. The mixture should be somewhat liquid. If necessary, add some more chicken stock.
Bring the chicken glace to a boil.
Pour the polenta into 4 bowls. Top with the cooked mushrooms. Drizzle with chicken glace.