Peel and finely chop the shallots and place them in a pan with 2-3 tablespoons of water. Cook them slowly until the water has evaporated, then add the butter. Allow the butter to melt (but not cook) and stir into the shallots.
Place the fillet of beef under a preheated moderately hot grill and cook for 7-8 minutes on each side. Place it on a warmed serving dish and cover with the shallots. Et Voila! Extremely simple but extremely succulent. Serve with French fried potatoes.