Prep the ingredients by washing and drying the fresh tarragon leaves and removing the leaves from the stems. Discard the stems. Finely mince the fresh tarragon.
Rinse and dry the rainbow trout.
Heat up a large frying pan over medium heat, one that will hold at least 2 of the trout fillets. How hot? This is important because you must be careful when adding oil or any fat to a heated pan.
While the pan is heating, season the skin side of the trout with salt and pepper.
When the pan is hot enough, add a tablespoon or two of oil to the pan and move the pan around so the oil coats the bottom. When the oil gets hot but not smoking, add the trout fillets skin side down.
While the trout is cooking, season the non-skin side with salt, pepper and some of the tarragon. Depending on the thickness of the fillets, cook for approximately 3 - 4 minutes until the skin is crispy.
Flip the trout fillets over and cook for 2 - 3 minutes or until the fish is perfectly cooked through. Transfer the cooked trout to a plate, loosely cover with foil to keep warm while you cook the remaining fillets.I like to bring the pan back to the stove, add a little oil if needed and let the pan and oil get hot again before adding the next pair of trout fillets. If the pan isn't hot, the skin will not crisp up as nicely as the first batch.
When all the rainbow trout fillets are pan fried, plate with your side dishes and serve.