In a large, heavy-bottomed pot or Dutch oven, heat 3 tablespoons (45ml) oil over medium-high heat until shimmering. Add cremini mushrooms and reserved rehydrated mushrooms (from stock) and cook, stirring, until lightly browned, about 8 minutes. Add onion and cook, scraping up any browned bits, until softened, about 3 minutes; lower heat if necessary to prevent scorching.
Stir in smoked paprika followed by stock. Bring to a simmer, then add collard greens, pushing down to submerge. Return to a simmer and cook, uncovered, until greens are very tender, about 30 minutes. Season with salt and pepper and add remaining ¼ cup (60ml) olive oil.
Add vinegar to taste, if desired, then serve. (You can add vinegar to the pot, or let individual diners season their greens with it at the table.)
