For the Fries: Combine potatoes, vinegar, and 2 tablespoons salt in a large pot and add enough cold water to cover by 1 inch. Bring to a boil over high heat, then reduce to a simmer and cook until potatoes are tender but still firm, about 10 minutes. Drain well and spread potatoes in a single layer on a wire rack set inside a rimmed baking sheet. Freeze until completely solid, at least 4 hours or overnight.

For the Steak: Season steaks generously with salt and pepper. Heat oil in a large cast iron skillet or stainless steel pan over high heat until shimmering. Add steaks and cook, flipping every 2 minutes, until deeply browned and an instant-read thermometer inserted into the thickest part registers 120°F (49°C) for rare or 125°F (52°C) for medium-rare, 8 to 12 minutes total. Add butter, thyme, and shallots (if using) to the pan during the last 2 minutes of cooking, basting the steaks with the melted butter. Transfer steaks to a cutting board and let rest for 10 minutes.

For the Green Peppercorn Sauce: While steaks are resting, pour off all but 1 tablespoon rendered beef fat from the skillet. Add butter to the skillet and melt over medium heat. Add green peppercorns and shallots and cook, stirring, until fragrant, about 1 minute. Whisk in flour and cook, stirring constantly, for 1 minute. Gradually whisk in beef stock and brandy, scraping up any browned bits from the bottom of the pan. Bring to a simmer and cook, stirring occasionally, until sauce has thickened, about 5 minutes. Stir in thyme sprig and heavy cream. Season with salt to taste. Remove thyme sprig before serving.

To Serve: Slice steaks against the grain. Arrange frites on plates alongside sliced steak. Spoon green peppercorn sauce over steak and serve immediately.