Preheat the oven to 200C/400F/Gas 6.
Season the lamb with salt and freshly ground black pepper. In a heavy frying pan, heat 3 tablespoons of the olive oil until it is nearly smoking. Add the lamb and cook over a high heat until browned all over. This should take about 5 minutes; the lamb loin should still be rare inside. Place on a wire rack and allow to cool to room temperature.
Pour the breadcrumbs onto a baking sheet and drizzle with the remaining olive oil. Mix gently with your fingers. Put into the oven and toast the crumbs until lightly browned, stirring two or three times. When browned, allow to cool, then add the herbs.
For the sauce, reduce the lamb stock until it has a light sauce consistency. Remove from the heat and stir in the herbs, mustard and butter. Check for seasoning.
To prepare the scallion crushed potatoes, cook the new potatoes in boiling salted water until tender, then drain. Melt the butter in a saucepan over a moderate heat, add the spring onions and a little salt and cook gently for one minute. Add the potatoes and crush gently with a fork. Keep warm.
While the potatoes are cooking, finish the lamb. Mix the two mustards together and brush over the top of each loin. Dip the mustard-coated part of the loin into the breadcrumbs and gently press the crumbs onto the mustard. Set the loins on a baking sheet, crumb-side up.
Place in the top of the oven and roast for 4-5 minutes for medium rare, or 8 minutes for medium-well done. Remove from the oven and allow to rest.
Heat a little oil in a pan and sauté the blanched carrots, lettuce and broad beans with the girolles for a few minutes. Season to taste with salt and freshly ground black pepper.
To serve, spoon the vegetable garnishes and some of the crushed potatoes onto the warmed plates. Slice the lamb, allowing three thick slices for each person, and place on the potatoes. Spoon over the sauce and garnish with fresh parsley.