Brook Trout Sauteed With Mushrooms

• 12 fillets with skin
• 6 trout (whole)
• 1/2 when (cleaned)
• 50 gr butter (unsalted)
• 40 gr all purpose flour
• 45 ml vegetable oil
• 60 ml milk
• 30 ml lime juice (fresh)
• 7 gr parsley (finely chopped fresh)
• 6 slices mushrooms