In a large mixing bowl, whisk together 2 tablespoons of the oil, the vinegar, honey, mustard, and 1 teaspoon salt. Pat the chicken dry and add it to the marinade, coating it well. Set aside at room temperature, stirring a couple of times while you make the onions.
Heat a large cast-iron or heavy skillet over medium-high heat until very hot, about 2 minutes. Add the onions in an even layer. Season with salt and cook, mostly undisturbed, for 4 minutes, stirring every minute or so. Add the mushrooms, season with salt, and stir to combine. Cook, mostly undisturbed, until the mushrooms shrink and start to brown, about 4 minutes, stirring every minute or so.
Stir in the remaining 2 tablespoons of olive oil and allow the onions and mushrooms to cook until the start to color, stirring and lowering the heat as necessary to avoid burning, about 4 minutes. Push the onions and mushrooms to the edges of the skillet, and add the chicken pieces to the center. Pour any remaining marinade (there will be very little) over the onions and mushrooms. Cook undisturbed for 4 minutes, then turn the chicken to brown on the other side for another 4 minutes or so. When the chicken is browned, stir it together with the onions and mushrooms and cook, stirring occasionally, until the chicken is cooked through, about 10 minutes more. (Reduce the heat to medium if the onions look like they are burning at any point.)
Serve over the noodles, topped with a sprinkle of parsley.