Heat half the olive oil in a large frying pan over medium-high heat.

Cook beef fillets on both sides until cooked to your desired doneness (e.g., medium-rare, medium).

Transfer cooked beef fillets to a warm oven to keep warm while preparing the sauce.

If using thick steaks, finish cooking them in the oven at a higher heat setting for about 15 minutes to ensure they are cooked to your desired doneness without burning the outside.

Heat remaining olive oil in the same pan.

Add finely chopped celery rib, crushed garlic cloves, and finely chopped brown onion to the pan.

Cook, stirring occasionally, until the vegetables soften.

Add dry white wine to the pan and stir, scraping up any browned bits from the bottom.

Cook until the liquid is reduced by half.

Add double cream, ground mixed peppercorns (or more to taste), and beef stock granules to the pan.

Bring the sauce to a boil, then reduce heat to low.

Simmer uncovered, stirring occasionally, for about 5 minutes, or until the sauce thickens slightly.

Stir in fresh thyme leaves.

Serve the pepper thyme sauce immediately over the beef fillet steaks.

Serve with your favorite vegetables and potato, or celeriac mash and a carrot casserole.