Season steaks and place in a hot frying pan with olive oil. Cook on both sides for a total of 5 -6 minutes, remove from pan and keep warm.
Keep pan on full heat and add wine. Boil to reduce by half then add the beef stock and reduce.
For the rarebit, place egg yolks, mustard and breadcrumbs in a bowl along with a bit of Worcestershire sauce and a dash of Tabasco. Stir in milk and beer and season. Grate Stilton cheese and fold in. mix everything together until a very thick paste has formed.
Preheat the grill to a high heat. Top steaks with rarebit and place under grill until golden brown on top. Remove from grill and place on four plates.
Season the reduced sauce and add butter to give a glaze. To finish, add pesto to the sauce, pour in around the steaks and serve.