Transfer cleaned mushrooms to a medium saucepan. Cover with water and bring to a boil. Turn heat to low and simmer for 5 minutes, covered. Drain and shake excess water. Save mushroom water for soup, sauce, other use or discard.
Using an blender, food processor or immersion blender (stick) puree the oil, vinegar, mustard, Italian seasoning, basil, oregano, sugar, salt, pepper flakes, shallots and garlic until smooth. Stir in the parsley (See Note 1).
Transfer warm, poached mushrooms to a bowl and pour dressing over them, tossing to coat (See Note 2). Cover with plastic wrap and refrigerate for 2 hours minimum, best overnight.
Serve cold or at room temperature and drained slightly, as an appetizer or as part of a mezze platter.