First, prepare the polenta. Preheat the oven to 425 degrees F. In a lidded baking dish, whisk together 3 cups water, the cornmeal,
1 1/4 teaspoon salt, and 1/8 teaspoon pepper. Cover, and bake for 30 minutes, stirring halfway through. Remove from the oven and add the milk and butter, and whisk until smooth.
Meanwhile, sprinkle the chicken breasts with 1/4 teaspoon each salt and pepper.
Heat 1 tablespoon of the oil in a large skillet over high heat.
Add the chicken; cook until lightly browned, 2 to 3 minutes per side. Transfer to a plate. Add the remaining tablespoon oil to the skillet. Add the mushrooms, garlic, and 1/4 teaspoon salt. cook over medium heat until the mushrooms are golden, 4 to 5 minutes. Pour the wine into the skillet; cook, stirring until evaporated, about 1 minute. Add the chicken broth and parsley; cook over medium high heat until the mushrooms are tender and the liquid has reduced, about 8 to 10 minutes. Return the chicken to the skillet. Cover; simmer over low heat until the chicken is cooked through, 10 to 12 minutes. Serve chicken and polenta topped with the mushroom mixture.