Season steaks with salt and ground black pepper.

Melt butter and vegetable oil in a preheated pan over medium-high heat.

Add steak and cook to desired doneness.

Remove steak from pan, wrap in tin foil, and set aside to rest.

Reduce heat to medium.

Add butter, crushed black peppercorns, and green peppercorns to the pan.

Fry for about 2 minutes.

Add flour to the pan, creating a roux with the pan juices.

Cook the roux for 30 seconds.

Gradually add beef stock, whisking constantly to prevent lumps.

Add cream, whisking to combine.

Simmer over low to medium heat until the sauce thickens to your liking.

Taste and add salt if needed.

Place steaks on plates.

Top each steak with a slice of cheddar cheese.

Spoon pepper sauce over the cheese.

Serve immediately with your favorite side dish.