Rub the fillet with olive oil and season well with salt and pepper.
Heat a griddle pan until smoking hot.
Brown the medallions on all sides, about 1-2 minutes per side.
Place the fillet medallions and broccoli into a baking dish and drizzle with a little olive oil, place into the oven for 10- 12 minutes, depending on how you enjoy your fillet.
Allow the fillet to rest for 5 minutes Add the tarragon, white wine and vinegar to a small pot and bring to a simmer, allow to reduce by half.
Sieve the mixture into a bowl over a pot of simmering water, discard the tarragon leaves.
Whisk in the egg yolks and continue whisking until the mixture thickens, about 8-10 minutes Slowly beat in the melted butter “little by little” and season with salt and cayenne pepper.
Serve the beef fillet with broccoli and a generous dollop of béarnaise sauce.