Place the potatoes in a large saucepan and add enough cold water to cover; bring to a boil.
Place all the peppercorns on a work surface. Using a small, heavy skillet, whack the peppercorns, then roll the skillet over the peppercorns to coarsely crush. Sprinkle the steaks with the kosher salt and coat with the crushed peppercorns.
When the water comes to a boil, salt the water, then cook the potatoes until they are just fork-tender, 6 to 8 minutes.
Meanwhile, heat a cast-iron skillet over medium-high. Add the oil, one turn of the pan. Add the steaks and cook until browned, turning once, about 6 minutes; transfer to a plate and cover to keep warm. Reduce the heat to medium; melt 2 tbsp. butter in the skillet. Add the shallots and garlic, season with salt and cook, stirring often, until softened, about 2 minutes. Add the cognac and swirl to blend. Add the stock and bring to a bubble. Add the cream and simmer until thickened, 3 to 5 minutes.
Drain the potatoes; return to the hot pot. Add 2 tbsp. butter and the herbs. Season with salt; toss to coat.
Arrange the steaks on plates; top with the sauce and the arugula. Serve each steak with 5 potato wedges.