Heat 2 tablespoons of the oil in a 12-inch nonstick skillet over medium high heat until just smoking. Add mushrooms and 1 teaspoon salt and cook, covered and stirring occasionally, until the mushrooms release their liquid and begin to soften, about 10 minutes. Uncover and continue to cook, stirring occasionally, until skillet is dry and mushrooms are lightly browned, about 5 minutes.
To the pan, add the shallot, garlic, oregano, and red pepper flakes. Cook until fragrant, about 1 minute. Stir in the vinegar and water and bring to a boil. Cook until liquid reduces by half, about 5 minutes.
In a medium bowl, whisk together the remaining 6 tablespoons oil, Dijon mustard, ¼ teaspoon salt, and ¼ teaspoon pepper.
Add the mushroom mixture to this bowl and stir to combine. Let cool completely. Stir in parsley.
Cover mushrooms and refrigerate until chilled, about 1 hour. Season with salt and pepper to taste before serving.
Mushrooms can be refrigerated up to 3 days.