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Take the cote de boeuf out of the fridge at least one hour before cooking to come to room temperature, then pat thoroughly dry with kitchen paper and season all over with sea salt flakes and freshly ground black pepper.
Place a heavy-based frying pan over a high heat until smoking hot, add the olive oil and let it shimmer.
Carefully place the seasoned cote de boeuf into the hot pan and sear for 3–4 minutes on one side until a deep golden-brown crust forms; flip and sear for another 3–4 minutes, then hold the steak upright with tongs to sear the fatty edges for about one minute per side.
Reduce the heat to medium, add the unsalted butter, crushed garlic cloves, fresh thyme sprigs and rosemary sprigs to the pan, tilt the pan and continuously baste the steak with the melting butter and aromatics for 5–7 minutes.
Insert a meat thermometer into the thickest part of the steak (away from the bone) and aim for 63 °C (145 °F) for medium-rare; if you prefer it more done or it is particularly thick, transfer the pan to a preheated oven at 180 °C (160 °C fan) for an additional 10–15 minutes.
Transfer the cooked cote de boeuf to a warm plate or board, tent loosely with foil and let rest for 10–15 minutes to allow the juices to redistribute.
Slice the cote de boeuf against the grain, carve off the bone, drizzle with any remaining pan juices and serve with your choice of sides.