For the beef:
1) Preheat the oven to 180°C/gas mark 4.
2) Sprinkle both sides of the beef with salt and pepper. Heat the olive oil in an oven-safe medium frying pan over high heat. When the oil is hot, carefully place the fillet in the pan. Cook until browned on both sides, about three to four minutes a side.
3) Transfer the steak to the oven and bake until a meat thermometer reads 55°C. For medium-rare, about five to six minutes. Remove the beef from the oven and let rest for five minutes.
For the sauce:
1) Heat the olive oil in a medium frying pan over medium heat. Add the mushrooms and the shallots and cook until golden brown and tender, about five minutes. Add the thyme, white wine, salt, and pepper and continue to cook until all of the liquid has evaporated, about five more minutes.
2) Meanwhile, put the gorgonzola, mayonnaise, and mustard in a food processor and combine until smooth. Transfer the gorgonzola mixture to the frying pan with mushrooms and shallots. Gently stir the cheese mixture into the mushroom mixture.
3) Slice the beef and serve topped with a dollop of the cheese sauce. Reserve leftover sauce for another use.