Soak mushrooms in room temperature water for 20 to 30 minutes to soften the mushrooms. Strain in a sieve or colander, reserving the soaking liquid in a separate bowl.

Run clean water over the mushrooms to remove any lingering grit. Squeeze the mushrooms lightly to remove as much water as possible, then roughly chop. Set aside.

Trim the chicken livers (kitchen shears work well), discarding any veins or stringy bits. Cut the livers into 1-inch (25 mm) pieces and season with ¼ each of salt and pepper.

Heat 1 tablespoon butter and olive oil in a wide skillet over medium-high heat.

Cook the livers, turning them until browned on both sides but still slightly pink on inside, about 4 to 5 minutes total. Remove from pan.

Add the vinegar to the pan to deglaze, using a spatula to loosen any bits of liver from the bottom of the pan. Add the remaining tablespoon of butter to the pan. After it melts, add the shallot and mushrooms. Season with the remaining salt and pepper as they cook.

After cooking the mushrooms and shallots for a few minutes, add ½ cup of the mushroom soaking liquid to the pan. Scoop the liquid from the top of the bowl, as any dirt from the mushrooms will have settled on the bottom of the bowl.

Cook the mushrooms a few minutes more. If they still seem too chewy, add another ½ cup of the mushroom soaking liquid and cook a few more minutes.

Add the chicken livers back to the pan. Toss with the mushrooms to reheat.

Stir in the parsley and thyme, then serve. If you like, garnish with a dollop of crème fraiche.