In a medium pot, combine the potatoes with enough water to cover; bring to a boil. Salt the water and cook the potatoes until tender, about 20 minutes. Drain and return the potatoes to the hot pot and cook off the excess moisture.
While the potatoes cook, heat a skillet over medium-high heat. Add 2 tablespoons EVOO, 2 turns of the pan. Add the bacon and cook until almost crisp, about 5 minutes. Add the shallots, lower the heat and cook until tender, 6 to 7 minutes. Add the vinegar and scrape up the browned bits from the bottom of the pan, then whisk in the mustard. Add the warm potatoes and half of the parsley, turning the potatoes until they are evenly coated and absorb the dressing. Keep warm.
Preheat a grill pan over high heat. Drizzle the steaks with some EVOO and season both sides with salt and pepper or grill seasoning. Grill the steaks, turning once, 7 to 8 minutes for rare or 12 minutes for medium-well. Let rest for 5 minutes before slicing.
In a medium skillet, heat the remaining 2 tablespoons EVOO, 2 turns of the pan, over medium-high heat. Add the mushrooms and scallion whites and cook until softened, 7 to 8 minutes. Add the wine and boil for 1 minute to reduce slightly. Stir in the butter until melted and remove from the heat. Slice the steaks against the grain and top with the mushrooms, the remaining parsley and the scallion greens. Serve the warm potato salad alongside.