Bring a large pot of salted water to a boil over a high flame. Add the dandelion greens and blanch until tender, about 3-4 minutes. Strain and rinse under cool water. Set aside. In a large sauté pan over a medium flame, heat 1 Tbsp. oil until hot. Add the shallots and stir until translucent, about 5 minutes. Add the mushrooms and continue to stir for another 2 minutes. Reduce the flame to low and continue to cook while stirring frequently, until the mushrooms are slightly browned and completely tender, about 8 minutes. Add the greens to the pan when the mushrooms are 2 minutes from being finished. Remove from heat and set aside. Meanwhile, in a sauce pan over a medium flame, bring 2 1/2 cups of water to a boil. Slowly whisk in the polenta along with a pinch of salt. Reduce the flame to low and continue whisking until the polenta is tender and thickened, about 15 minutes. At the last minute, whisk in the remaining oil along with the caramelized onions. Divide the polenta between 2 plates. Top evenly with the greens and mushrooms. Garnish with the cheese, if desired.