Crack the peppercorns with a mortar and pestle. It's fine if some are just broken in half and others are smaller; the important thing is to crack them all. If you don't have a mortar and pestle, crack the peppercorns on a cutting board, crushing them with a meat pounder or the bottom of a small heavy skillet or saucepan.
Sprinkle 1 tsp. of the thyme and 1 tsp. salt evenly on both sides of the steaks and then pat the peppercorns on both sides to create a thin crust. Let the steaks sit at room temperature for 30 minutes.
Position a rack in the center of the oven and heat the oven to 425°F.
Turn on the stove's exhaust fan. Heat a heavy-duty 10- or 11-inch ovenproof skillet (preferably cast iron) over medium-high heat for 2 minutes. Add the oil; when it's shimmering hot, arrange the steaks in the pan and cook until the bottom sides are nicely browned and release easily from the pan, 2 to 3 minutes. Flip the steaks and cook the other sides until browned, 2 to 3 minutes more.
Transfer the skillet to the oven and cook the steaks until an instant-read thermometer inserted in the center reads 125°F for rare, 130°F for medium rare, and 135°F for medium, 4 to 7 minutes. Transfer the steaks to a plate and tent with foil.
Pour off any fat left in the pan, but not the browned bits. Melt the butter in the skillet over medium heat. Add the shallot and cook, stirring and scraping the bottom of the pan, until softened, about 2 minutes. Remove the pan from the heat to avoid any flare-ups and carefully add 1/3 cup of the Cognac. Return the pan to medium heat and cook until the Cognac reduces to a glazy consistency, 1 to 2 minutes.
Add the cream, tarragon, the remaining 1 tsp. thyme, and any accumulated juices from the resting steaks. Bring to a boil, reduce to a simmer, and cook, stirring frequently, until slightly reduced, 1 or 2 minutes more. Stir in the remaining 1 tsp. Cognac and season to taste with salt. Spoon the sauce over the steaks and serve.