Pull the steak from the fridge about an hour before cooking. Pat it bone-dry with paper towels and season generously with kosher salt and black pepper on all sides. A good rule of thumb is about 30% more salt than you'd normally use.
Heat a cast iron skillet over high heat until it's ripping hot.
Add the oil to the hot pan and swirl to coat. Lay the steak in away from you so any splatter goes away from your hand.
Set a steak weight on top for even contact. Sear about 3 minutes per side.
Take the steak off and rest it on a wire rack for 6 minutes, the same time it spent in the pan. This lets the inside catch up to the outside.
Wipe the pan clean to clear the browned bits, add fresh oil, and reheat until ripping hot again.
Return the steak with the weight and sear another 3 minutes per side.
Rest again for 6 minutes, then check the internal temperature. You're looking for about 118–120°F at this stage (carryover will keep climbing, so re-check before the next round).
Wipe the pan and add fresh oil one more time, back up to high heat.
Return the steak to the pan and add the butter, smashed garlic, and thyme.
Let the butter melt to a golden brown, then drop the heat to medium-high the moment it's melted so it browns without burning.
Tilt the pan and spoon the brown butter over the steak, basting continuously. Keep that frying sound going so you don't lose temperature.
Flip and keep basting until the internal temperature reaches about 125°F for medium-rare.
Move the steak to a cutting board and spoon the butter, garlic, and thyme over the top. Let it rest while you build the sauce.
With the pan still hot, turn off the heat and add the minced shallot straight into the fond. Stir until softened and picking up the brown bits. The shallot's own water deglazes the pan safely.
Transfer the shallot and fond to a small saucepan over medium heat. Add the peach halves and the white balsamic and stir.
Let the peaches break down for 3–4 minutes, stirring. Watch closely, the sugar burns fast. You want them falling apart but still holding some texture.
Add a shot of bourbon and let it cook off completely. Taste as you go. When the astringency is gone and it turns warm, round, and caramel, it's ready.
Finish with the remaining butter, a squeeze of lemon, and a few torn basil leaves. Season with a pinch of salt and pepper. Turn off the heat.
Remove the bone from the steak (watch for a small sliver from the band-saw cut). Slice against the grain into thick pieces.
Arrange the slices on a plate and spoon the peach sauce over the center.
Finish with flaky salt and serve.