In a large sauté pan, melt ¼ cup butter over medium-high heat. Add shrimp, and cook for 2 minutes. Add garlic, salt, cayenne, and black pepper. Cook, shaking pan occasionally, for 2 minutes. Add sherry, and cook for about 1 minute. Drain shrimp mixture, and let stand until cool.
Cut remaining 1¾ cups butter into small cubes. In the work bowl of a food processor, place shrimp mixture; pulse until finely chopped. Add butter, and blend very well. Cover and refrigerate shrimp butter until chilled. (This can be done up to 3 days in advance.)
In a large stockpot, heat milk over medium-high heat until hot but not boiling. Slowly whisk in polenta. Cook, stirring constantly, until thickened, about 10 minutes. Reduce heat to low, and cook, stirring occasionally, until polenta is tender and doesn’t have a raw corn flavor. Whisk in shrimp butter, and season to taste with salt.
Meanwhile, in a large bowl, toss together mushrooms, oil, thyme, and a large pinch of salt. Spread on a baking sheet in an even layer.
Bake until mushrooms start turning a light golden brown, 8 to 10 minutes. Place in a large bowl, and toss with parsley. Taste for seasoning. Serve hot mushrooms over hot polenta.
Recipe by Louisiana Cookin' at https://louisianacookin.com/shrimp-polenta-roasted-mushrooms/