Bring the steak to room temperature for 20–30 minutes. Pat dry and season both sides with salt and lots of freshly cracked black pepper.

Preheat a heavy skillet (cast iron preferred) over medium-high heat for 3–5 minutes until hot. Add oil and swirl.

Place the steak in the hot pan and cook undisturbed for about 3–4 minutes until a brown crust forms. Flip and cook another 3–4 minutes for medium-rare.

During the last minute, add 1 tbsp butter to the pan and baste the steak. Remove the steak to a cutting board and tent loosely with foil. Rest for 5–10 minutes.

Wipe out excess fat from the pan, leaving browned bits, and lower heat to medium. Add remaining 1 tbsp butter.

If using shallot/garlic, sauté for 30–45 seconds until fragrant.

For sunny-side or over-easy eggs: crack the eggs into the skillet, season with salt and pepper, and cook for 2–3 minutes until whites set but yolks remain runny. Sprinkle cheese and cover the pan for 30–60 seconds to melt.

For scrambled eggs: beat eggs with salt and pepper, pour into the pan, and stir gently until soft curds form (about 1–2 minutes). Stir cheese in off heat.

After removing the eggs, deglaze the pan with beef stock or red wine, scraping up brown bits. Stir in Dijon mustard and simmer until slightly reduced.

Slice the T-bone against the grain and plate with the peppery cheese eggs on the side. Garnish with additional pepper and chopped herbs.