In a large skillet or Dutch oven, heat olive oil and butter over medium heat. Add the chopped onion and cook until softened, about 5-7 minutes. Add the minced garlic and fresh thyme and cook for another minute until fragrant.

Increase the heat to medium-high, add the sliced mushrooms to the skillet. Cook, stirring occasionally, until they release their liquid and begin to brown, about 10-12 minutes.

Pour in the white wine to deglaze the pan, scraping up any browned bits from the bottom. Let it simmer until the wine has almost completely evaporated. Season with salt and pepper, then remove from heat and set aside.

In a medium saucepan, bring the vegetable broth and milk to a simmer over medium-high heat.

Once simmering, slowly pour in the polenta while whisking continuously to prevent lumps from forming.

Reduce the heat to low and continue to cook, stirring frequently with a wooden spoon, until the polenta is thick and creamy, about 20-25 minutes.

Remove the polenta from the heat and stir in the unsalted butter and grated Parmesan cheese until fully melted and incorporated. Season with salt and pepper to taste.

Preheat your oven to 375°F (190°C). Lightly grease a 9x13 inch baking dish.

Spread the creamy polenta evenly into the bottom of the prepared baking dish.

Spoon the savory mushroom ragout over the polenta in an even layer.

Sprinkle the shredded Gruyère cheese evenly over the mushroom layer.

Bake for 20-25 minutes, or until the casserole is heated through and the cheese is melted, bubbly, and lightly golden.

Let the casserole rest for 5-10 minutes before serving. This allows it to set up slightly, making it easier to serve. Garnish with fresh parsley if desired.