Nutrition: Per serving
First, make the butter. Tip the tarragon stems, shallots, vinegar and some black pepper into a small saucepan, and bring to the boil. Reduce the heat to a simmer and cook for 10 mins, or until the vinegar has reduced to about 2 tbsp. Remove from the heat and leave to cool completely, then remove and discard the tarragon stems. Tip into a bowl with the softened butter and tarragon leaves. Season with salt and mash everything together to combine. Spoon the flavoured butter onto a sheet of baking parchment, roll into a log and twist the ends to secure. Chill until firm. Will keep chilled for up to five days or frozen for three months.
Heat the oven to 220C/200C fan/gas 7. Season the beef generously with salt, then brush all over with mustard and roll in the crushed peppercorns to coat. Sit the joint, fatty-side up, in a roasting tin that provides a snug fit. Roast for 20 mins, then reduce the oven temperature to 190C/170C fan/gas 5 and roast for 35-40 mins more, for rare, or until a probe thermometer reaches 50C. For medium-rare, roast for 45 mins or until the beef reaches 55C, or for medium, 50 mins until the beef reaches 60C. Remove the beef from the oven, lift onto a platter or board that can catch its juices, and leave to rest somewhere warm for 15-30 mins. Meanwhile, bring the butter to room temperature. Tip the beef resting juices into your gravy, then carve the beef as thinly as possible and drape the slices over a serving platter. Season and top with slices of the béarnaise butter, then flash briefly under the grill just to melt it.
