In a large saucepan over high heat, bring broth to a boil. Slowly pour in polenta, whisking constantly to prevent clumping.
Reduce heat to a simmer. Use a wooden spoon to stir almost constantly, adding more broth as needed if mixture becomes too dry. Refer to polenta package for cook times.
Once polenta is cooked and creamy, add cheese, butter, salt and pepper.
Mushrooms
Clean mushrooms with a small brush or damp paper towel - do not rinse under water.
Cut off and discard woody stems from mushrooms. Slice mushrooms into ¼ inch thick pieces.
Heat 1 tablespoon olive oil in a skillet over medium heat. Cook shallot and fennel in hot oil until lightly browned, abut 3-5 minutes. Add garlic and cook until fragrant, about another minute. Transfer to a bowl and set aside.
In the same skillet, heat 1 tablespoon olive oil. Add half of the mushrooms to the pan in a single layer. Season generously with salt and pepper. Sauté mushrooms until they begin to caramelize and crisp up, 3-5 minutes. Pour into bowl with fennel and set aside. Repeat with remaining mushrooms.
Place mushrooms and fennel mixture back in pan and add wine to pan. Use wooden spoon to scrape up any browned bits inside of the pan. Once wine is mostly absorbed, add broth and bring to a simmer over medium heat. Add butter and whisk quickly to combine liquids.
Serving
Move polenta to a serving dish. Spoon mushrooms evenly on top of polenta, then garnish with fresh basil and grated fresh Pecorino Romano cheese. Serve immediately or place in oven to keep warm.
Notes
Use a low simmer when cooking polenta to prevent clumps and ensure a smooth, creamy texture.Roast mushrooms at a high temperature to achieve a caramelized, savory flavor while keeping their texture firm.