Step 1: Melt butter in a large, heavy skillet over moderate heat.
Step 2: Add shallots and cook, stirring frequently, until soft but not brown, about 5 minutes.
Step 3: Stir in parsley, chervil, thyme and tarragon.
Step 4: Add wine and mix well.
Step 5: Remove from heat.
Step 6: Sprinkle trout with salt and pepper.
Step 7: Arrange on top of herbs in skillet in a single layer, overlapping slightly if necessary.
Step 8: Cut a circle of foil large enough to fit the skillet and press it gently but firmly on top of the fish.
Step 9: Return skillet to moderate heat and simmer for about 5 minutes, or until cooked through.
Step 10: Remove fish to a platter and cover with fresh foil to keep warm.
Step 11: Bring liquid in skillet to a boil over high heat, stirring or whisking constantly.
Step 12: Cook until reduced to a thin film that barely covers bottom of pan.
Step 13: Reduce heat to moderate.
Step 14: Stir in cream and any liquid accumulated from the fish.
Step 15: Continue to cook, stirring occasionally, until thick enough to coat the whisk heavily, 5-10 minutes.
Step 16: Cover trout with sauce.
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