In a medium soup pot or Dutch oven, heat the olive oil, two turns of the pan, over medium-high. Add the mushrooms and thyme and cook, stirring occasionally, until the mushrooms brown, about 8 minutes; season with salt and pepper. Add the shallots and garlic; stir until the shallots soften, 1 to 2 minutes. Add the escarole. Stir until wilted, about 4 minutes. Add the stock, beans and the cheese rind, if using. Bring the soup to a low rolling boil over high. Reduce the heat a bit and let simmer until the flavors meld, about 15 minutes.
Remove the soup from the heat. Discard the rind, if using, and stir in the lemon juice. Ladle the soup into shallow bowls, then top with the grated Parm and a fat drizzle of EVOO.