Gently wipe each mushroom with a clean paper towel to remove any dirt or debris. Trim the stems as needed. If any mushrooms are significantly larger, cut them in half while leaving the smaller ones whole.
Place a large 12-inch sauté pan or cast iron skillet on the stove while still cold. Add the mushrooms along with ¼ cup of room-temperature water. Turn the heat to medium-high and cook, stirring occasionally, until the water evaporates and the mushrooms develop a deep golden-brown color. This process should take approximately 8 minutes. Stir periodically with a wooden spoon to ensure even browning.
While the mushrooms are cooking, combine the shallots, garlic, thyme, salt, and black pepper in a small bowl and set aside.
Once the mushrooms are well-browned and the water has nearly evaporated, drizzle in the olive oil. Continue cooking over medium-high heat, stirring occasionally, until the mushrooms take on an even deeper color and a slightly crisp exterior, about 4 more minutes.
Push the mushrooms to one side of the pan, creating space in the center. Add the butter and allow it to melt. Once fully melted, add the reserved shallot, garlic, thyme, salt, and black pepper directly into the butter. Sauté for about 1 minute, stirring frequently, until the shallots turn lightly golden and aromatic.
Deglaze the pan by pouring in the Worcestershire sauce, stirring continuously for about a minute. Then, add the broth and give the mushrooms another quick stir. Let the liquid simmer and reduce by about half, approximately 2 minutes. Once the sauce has thickened slightly and clings to the mushrooms, turn off the heat.
Transfer the mushrooms to a serving dish. Finish with a touch of freshly ground black pepper and adjust salt to taste. Garnish with a few sprigs of fresh thyme for an extra layer of flavor. Serve warm.