How to Make It
Bring the water and 1 teaspoon of the salt to a boil in a heavy saucepan over high. Whisk in the polenta and cook, whisking constantly, 45 seconds. Scrape the bottom and sides of the saucepan. Return to a boil; cover and reduce heat to medium-low. Cook until tender, 25 to 30 minutes, stirring occasionally. Stir in 1 tablespoon of the butter until melted. Set aside.
Meanwhile, melt the remaining butter in a large nonstick skillet over medium-high. Add the mushrooms; cook, stirring occasionally, until golden brown, about 10 minutes. Stir in the shallot and the remaining salt; cook 2 minutes.
Toss the greens with the oil and lemon juice. Top the polenta with the mushroom mixture, greens, and Parmesan.