Cover dried porcini mushrooms in warm water and let stand at room temperature until softened, 30 minutes to 1 hour.
In a large skillet over medium heat, heat oil until shimmering. Add parsley, garlic, and scallions and cook until tender, about 5 minutes.
Stir in rice and cook until the edges are translucent, about 3 minutes. Stir in porcini, shiitake, and cremini mushrooms. Cook until mushrooms are tender, about 3 minutes.
Reduce heat to medium and stir in 1 cup broth. Cook uncovered, stirring frequently, until broth is absorbed, about 5 minutes.
Stir in remaining broth, 1/2 cup at a time, cooking about 3 minutes after each addition and stirring occasionally, until broth is absorbed, rice is tender and mixture is moist.
Stir in cheese and vinegar and garnish with parsley if desired.