Heat a large straight-sided skillet over medium high heat. Add the oil and heat another 30 seconds. Add the shallot and 1/2 teaspoon of the salt to the hot pan and cook, stirring often, for 2 minutes or until fragrant and beginning to soften. Add the mushrooms to the pan along with another 1/2 teaspoon salt and the thyme. Cook, stirring often, until the mushrooms have let off some of their juices are beginning to brown, about 10 minutes.
Deglaze with the Marsala, if using, and add the broth and remaining salt. Reduce the heat to low to maintain a gentle simmer. Cover and cook for 5 minutes. Uncover the pan, increase the heat to medium and cook until the liquid has reduced by half, about an additional 5 minutes. Discard the thyme sprigs, stir in the butter and serve.
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