Pat steaks dry with paper towels and season with sea salt and fresh cracked pepper on both sides. Massage the seasoning into the steaks and let rest for 20 minutes.
Crush additional 1 Tbsp. peppercorns with a mortar and pestle. Crush the garlic, chop the shallot, and divide the butter.
Heat a cast iron skillet over medium-high flame. Once warm, add olive oil. When shimmering, add steaks. Cook 3-4 minutes per side to develop a crust.
Reduce heat to low, add garlic, 1 Tbsp butter, and thyme sprigs. Tilt pan to spoon butter and juices over the steaks several times.
Transfer steaks to a cutting board to rest for 10 minutes.
In the same skillet, add shallots and stir until lightly browned. Add crushed peppercorns and remaining butter. Simmer for 2 minutes, stirring frequently.
Remove from heat and add Cognac carefully (avoid flames). Return to low heat and let Cognac reduce by half, then add heavy cream. Simmer until sauce coats the spoon.
Add steak drippings to the sauce. Slice steak against the grain, plate, and spoon sauce over steak generously.