Melt 2 Tbs. of the butter in a 3-quart saucepan over medium-low heat. Add the shallots and cook, stirring often, until softened, 3 to 5 minutes. Add the wine, raise the heat to medium high, and cook until almost evaporated, about 2 minutes. Add the broth and potato and bring to a boil. Lower the heat to medium low, cover, and cook until the potatoes are tender when poked with a fork, 6 to 8 minutes. Add the peas, cover the pan, and cook until heated through, about 5 minutes more.
Purée the soup in 2 batches in a blender until very smooth. Reheat the soup in a 2-quart saucepan over medium-low heat. Add the Parmigiano, the remaining 1 Tbs. butter, and 1/2 tsp. pepper and cook, stirring, until melted. Serve drizzled with the truffle oil, if using.
Make Ahead Tips
The soup can be made a day ahead and refrigerated, covered.
nutrition information (per serving):
Photo: Scott Phillips