Step 1

Place racks in upper and lower thirds of oven; preheat to 325°. Combine mushrooms, thyme sprigs, and garlic on a large rimmed baking sheet. Season generously with kosher salt and pepper; drizzle with oil. Toss to coat mushrooms, then spread out in an even layer. (Make sure not to crowd the mushrooms on the baking sheet; otherwise, they’ll steam instead of getting crispy.) Transfer to upper rack in oven and let mushrooms roast while you prepare polenta.

Step 2

Bring 4½ cups water to a simmer in a large ovenproof saucepan over medium-high heat. Add butter and a generous pinch of kosher salt and whisk to melt butter. Gradually add polenta, whisking constantly. (Gradually incorporating the polenta into the water is key to preventing clumps.) Return mixture to a boil, immediately cover pot, and transfer to lower rack in oven. Bake polenta, shaking baking sheet with mushrooms occasionally, until polenta is tender, 25–30 minutes.

Step 3

Remove polenta from oven. Crank up oven temperature as high as it will go (but don’t broil). Continue to cook mushrooms until crisp around the edges, 5–10 minutes longer.

Step 4

Meanwhile, carefully uncover polenta and whisk vigorously, scraping bottom of pan, until polenta is smooth and thick. Gradually add 4 oz. Parmesan, whisking constantly until melted and incorporated; taste and season with more kosher salt and pepper. Cover and keep warm over low heat while mushrooms finish roasting.

Step 5

Remove mushrooms from oven; drizzle with vinegar. Toss to coat; let cool slightly.

Step 6

Divide polenta among bowls and top with mushrooms, thyme leaves, sea salt, and more Parmesan.