Steam the potatoes until tender, 12 to 15 minutes. Toss with 2 tablespoons of the butter and season with ½ teaspoon each salt and pepper.
Meanwhile, heat the oil in a large skillet over medium-high heat. Season the steak with ½ teaspoon each salt and pepper and cook until medium-rare, 3 to 5 minutes per side. Transfer to a cutting board and let rest for 5 minutes, then slice across the grain.
Return the pan to medium heat. Add the shallots, cornichons, mustard seeds, and the remaining butter. Cook, stirring often, until the shallots are soft, 3 to 5 minutes. Add the broth and cook, stirring often, until reduced by about half, 2 to 3 minutes. Stir in the vinegar, parsley, and ¼ teaspoon each salt and pepper. Serve the sauce over the steak and potatoes.