Pat the mushrooms completely dry with paper towels.
Whisk together the Dijon mustard, red wine vinegar, garlic, and honey. Slowly whisk in the olive oil. Season and stir in the parsley. Set aside.
Heat the olive oil in a large, heavy skillet over medium-high heat until shimmering.
Add the mushrooms in a single, even layer, cut-side down, without overcrowding the pan. Work in batches if needed.
Cook undisturbed 4 to 5 minutes, until deeply golden. Stir and continue cooking 4 to 5 minutes more, until browned all over.
Season the mushrooms with salt and pepper.
Transfer the hot mushrooms to a bowl and toss with the Dijon mustard dressing while still warm.