2) With the motor running slowly, drizzle in the olive oil until you have a thick sauce. Season with salt and pepper and the sauce is ready to serve.
For the beef:
1) A half-hour before cooking, remove the fillets from refrigerator. Prepare a barbecue or a griddle pan with a medium-high heat.
2) Brush the meat lightly with olive oil and season with salt and pepper. Place the fillets on the griddle and cook, without moving, until griddle marks appear, about 4 mins.
3) Turn the fillets and continue to griddle until an instant-read thermometer inserted into the fillets sideways registers about 50 degrees C, about 3 to 4 mins more. Set aside on a cutting board to rest for 5 mins before serving.
4) Divide the fillets among the plates and drizzle with some of the sauce. Pass the remaining sauce at the table.