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Pat steaks dry with paper towels. Season all over with kosher salt and a generous amount of ground pepper. Let sit 15–30 minutes.
Coarsely crush peppercorns with a mortar and pestle or place in a resealable plastic bag and crush with a small saucepan (they should be a lot coarser than ground pepper).
Heat oil in a large skillet, preferably cast iron, over medium-high. Cook steaks, undisturbed, until a deep golden brown crust forms underneath, about 3 minutes. Turn over and cook on second side until golden brown, about 3 minutes. If the steaks have a fat cap, stand them on their sides with tongs and cook until browned, about 3 minutes.
Reduce heat to medium-low. Add smashed garlic cloves, thyme sprigs, and 1 Tbsp. butter to the pan. Cook, basting steak continuously, until an instant-read thermometer inserted into the thickest part of each steak registers 120°, about 2 minutes. Transfer steaks to a cutting board and let rest 10 minutes.
Meanwhile, combine shallot, sliced garlic, crushed peppercorns, and remaining 2 Tbsp. butter in skillet and cook, stirring often, until shallot and garlic are softened but not browned, about 5 minutes.
Remove from heat and add cognac to pan. Set over medium heat and cook until cognac is mostly evaporated and spoon leaves streaks in skillet while stirring, 1–2 minutes. Add cream, bring to a simmer, and cook until sauce coats spoon, about 1 minute. Season with kosher salt.
Slice steaks against the grain and transfer to a platter. Pour any juices from cutting board back into skillet and stir into sauce. Spoon sauce generously over steak; sprinkle with sea salt.