Step 1
Pat two 1½”-thick New York strip steaks (about 1½ lb. total) dry with paper towels. Season all over with kosher salt and a generous amount of freshly ground pepper. Let sit 15–30 minutes.
Step 2
Coarsely crush 1 Tbsp. whole black peppercorns with a mortar and pestle or place in a resealable plastic bag, seal, and crush with a small saucepan (they should be a lot coarser than ground pepper). Set crushed pepper aside.
Step 3
Heat 2 Tbsp. vegetable 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 and cook until golden brown on other side, about 3 minutes. If steaks have a fat cap, using tongs, stand them on their sides and cook until browned, about 3 minutes.
Step 4
Reduce heat to medium-low and add 3 sprigs thyme, 2 garlic cloves, smashed, and 1 Tbsp. unsalted butter to skillet. Cook, basting steak continuously with fat with a spoon, 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.
Step 5
Meanwhile, combine 1 large shallot, finely chopped, 2 garlic cloves, thinly sliced, remaining 2 Tbsp. unsalted butter, and reserved crushed peppercorns in skillet and cook, stirring often, until shallot and garlic are softened but not browned, about 5 minutes.
Step 6
Remove pan from heat and add ⅓ cup cognac, dry sherry, or brandy. Set over medium heat and cook until cognac is mostly evaporated and spoon leaves a track in sauce while stirring, 1–2 minutes. Pour in ½ cup heavy cream, bring to a simmer, and cook until sauce coats spoon, about 1 minute. Season with kosher salt.
Step 7
Slice steaks against the grain and transfer to a platter. Pour any juices from cutting board back into pan and stir into sauce. Generously spoon sauce over steak; sprinkle with flaky sea salt.
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