01 - Combine water and milk in a large saucepan and bring to a gentle simmer over medium heat. Add salt.
02 - Slowly whisk in the cornmeal, reducing heat to low. Stir frequently and cook until mixture thickens and is creamy, about 25 to 30 minutes.
03 - Incorporate butter, Parmesan cheese, and black pepper into the polenta. Adjust seasoning as needed. Cover and keep warm.
04 - Heat olive oil and butter together in a large skillet over medium-high heat. Add shallot and sauté until translucent, about 1 minute.
05 - Add minced garlic and cook for 30 seconds, then add sliced mushrooms. Sauté, occasionally stirring, until mushrooms are golden and moisture has evaporated, about 6 to 8 minutes.
06 - Pour in white wine and add thyme. Cook until most of the wine has evaporated, around 2 minutes. Season with salt and pepper, then remove from heat and stir in parsley.
07 - Divide the creamy polenta into bowls. Top with the sautéed wild mushrooms and garnish with extra thyme leaves and Parmesan if desired.