1 stick plus 1 tablespoon unsalted butter
6 tablespoons extra-virgin olive oil
3 medium shallots, thinly sliced (1 1/2 cups)
3 pounds mixed mushrooms, such as cremini, oyster, and stemmed shiitake, thickly sliced or quartered
3/4 cup brine, strained from a jar of dill pickles
Kosher salt
Pepper

In a very large skillet, melt 3 tablespoons of the butter in 2 tablespoons of the olive oil over moderately high heat, swirling, until the butter is golden, about 2 minutes. Add 1/3 of the shallots to the skillet and cook, stirring, until softened, about 1 minute. Add 1/3 of the mushrooms and cook, stirring occasionally, until tender and golden, 5 to 7 minutes. Add 1/3 of the pickle brine and cook until absorbed, about 1 minute. Transfer the mushrooms to a serving bowl and keep warm. Repeat the process 2 more times with the remaining butter, olive oil, mushrooms and pickle brine. Season the mushrooms with salt and pepper to taste and serve.