Bring 4 cups of water to a boil. Whisk in the polenta. Once it begins to thicken, reduce heat to a simmer and cook for 45 minutes until creamy and thick, stirring occasionally to prevent sticking. Stir in a 1/4 teaspoon of salt and the parmesan until melted and no longer visible. Remove from heat. Line an 8×11” baking dish with aluminum foil and carefully pour the polenta into the baking dish, using a spatula to smooth it to an even thickness, about 3/4″. Cover and refrigerate for at least two hours and up to two days until firm.

While the polenta chills, make your ragu. In a large heavy skillet heat the olive oil until shimmering over medium heat. Add the onion and garlic and saute until fragrant and translucent, about 5 minutes. Stir often and don’t allow them to brown. Add in the mushrooms and thyme and cook over medium high heat until the mushrooms start to release their liquid. Add 1/2 teaspoon of salt and continue to cook another 5 minutes until they begin to soften more. Stir in the flour and cook, stirring, until it is no longer visible, about 1 minute. Add in the wine, cream, and sugar, and bring the mixture to a simmer. Taste and adjust salt if desired. Simmer until thick and creamy and the mushrooms are nicely coated, about 10 minutes. Finish with a squeeze of fresh of fresh lemon juice and 1/2 cup minced parsley. Set aside and cover to keep warm.

Slice your polenta into squares—whatever size you desire—or use a biscuit cutter to cut shapes. Wipe down your pan, coat it lightly with olive oil, and heat it over medium-high. Fry the squares in the pan until golden brown on both sides and warmed through, about 5 minutes per side. Top the squares with warm mushroom ragu and serve immediately.