Trim 1 ½ pounds mushrooms (if using shiitake mushrooms, remove their stems completely) and slice into ¼-inch-thick pieces. Dice 1 medium yellow onion. Mince 3 garlic cloves. Pick the leaves from 1 small bunch of fresh parsley until you have 2 tablespoons and coarsely chop. Pick the leaves from 1 small fresh thyme bunch until you have 1 tablespoon.

Melt 2 tablespoons of the unsalted butter in a large high-sided skillet over medium heat. Add the onion and sauté until golden and softened for about 5 minutes. Add the garlic and thyme and sauté until fragrant, about 1 minute. Transfer to a medium bowl.

Add 1 tablespoon of the unsalted butter to the pan and add half the mushrooms in an even layer. Put the lid on the skillet and cook undisturbed until browned on the bottom, about 5 minutes. Take the lid off. Season with ½ teaspoon of the kosher salt and ¼ teaspoon of the black pepper and cook, stirring once or twice, until the mushrooms are browned all over and tender, 2 to 3 minutes more. Transfer to the bowl with the onion.

Add the remaining 1 tablespoon unsalted butter to the pan and repeat cooking the remaining mushrooms as above. Season with the remaining ½ teaspoon kosher salt and ¼ teaspoon black pepper. Return the cooked mushrooms and onion and any accumulated juices in the bowl to the pan.

Add ½ cup dry white wine and simmer, scraping up any browned bits from the bottom of the pan with a wooden spoon, until the liquid has evaporated, and the pot is almost dry for about 3 minutes. Add 1 tablespoon tomato paste and stir until it coats the mushrooms and onions and darkens in color, about 2 minutes.

Sprinkle 1 tablespoon all-purpose flour or cornstarch into the pan and toss to coat. Add 1 cup low-sodium vegetable broth or water, 1 tablespoon low-sodium tamari or soy sauce, 1 tablespoon Dijon mustard, and ½ teaspoon paprika. Stir and bring to a boil. Reduce the heat to low and simmer until the mixture is reduced slightly and is saucy, 4 to 6 minutes.

Remove the pan from the heat. Add the parsley and stir to combine. Taste and season with more kosher salt and black pepper as needed. Serve over cooked wide egg noodles, mashed potatoes, or steamed rice. Garnish each serving with 1 tablespoon crème fraîche or sour cream.