In a 12x7-inch baking dish, combine ½ cup of the yoghurt, water, oil, and ¼ teaspoon of the dill weed. Place salmon on top and turn to coat evenly with marinade; cover and chill for 1 hour. Remove salmon and discard marinade.
Using direct medium heat, grill or broil fish just until translucent (to test, slide a knife into the flesh and twist it to separate layers to see inside) and firm to the touch, about 8 to 10 minutes. Flip 2/3 of the way through cooking time.
Meanwhile, in a small saucepan, melt butter over low heat. Stir in remaining ½ cup yoghurt, ¼ teaspoon dill weed, and egg. Over low heat, cook and stir until thickened. Do not boil. Serve warm over salmon. Refrigerate leftovers.
Makes 4 servings.
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