How to Make It
Combine the shallots and wine in a heavy saucepan and boil over high heat until reduced to 2 tablespoons, about 45 minutes. Add the demiglace and boil until reduced to 2 cups, 10 to 15 minutes. Strain the sauce and return it to the saucepan.
Preheat the oven to 425°. Spread the potatoes in a medium baking dish and bake for 35 minutes, or until tender. Meanwhile, in a small skillet, cover the pearl onions with water. Add 2 tablespoons of the butter, the sugar and a pinch of salt and bring to a boil over high heat. Cook until the water has evaporated, about 20 minutes. Stir constantly until the onions are glazed and lightly browned, about 3 more minutes.
In a saucepan, cover the carrots with cold water. Add salt and bring to a boil over high heat. cook until just tender, about 7 minutes. Drain, rinse under cold water and drain again. Melt the remaining 1 1/2 tablespoons of butter in the saucepan, add the carrots and sauté until warmed through. Add the onions.
Meanwhile, light a charcoal grill or preheat the broiler. Brush the mushrooms with olive oil, season with salt and pepper and grill or broil for about 7 minutes per side, or until tender and lightly charred. Let cool slightly, then slice the mushrooms. Season the beef with salt and pepper and grill or broil for about 5 minutes per side for rare meat.
In a bowl, combine the chervil, parsley, chives and tarragon. Add the oil and vinegar, season with salt and pepper and toss well.
Rewarm the potatoes in the oven and the onions and carrots on the stove. Reheat the sauce. Set a beef fillet on each plate, top with the herb salad and spoon the sauce around. Arrange the mushrooms, potatoes, onions and carrots alongside the beef and serve.