Pat fillets dry with a kitchen towel. Season with salt and pepper on both sides. Set aside.
Heat a non-stick or cast iron pan over medium-high heat. Once heated add olive oil and butter to the pan.
In the preheated pan, place the fillets skin side down (if applicable) for about 2 minutes until golden brown.
Reduce the heat to medium and flip the fillet. Add fresh tarragon to the pan and cook until internal temp reaches 145°F. Cooking time will vary depending on how thick your fillet is.
Meanwhile, prepare the tarragon cream sauce.
Heat butter in a saucepan over medium heat.
Add 2 tbsp of butter to the saucepan.
Once melted, add the diced yellow onion (or shallot) and cook for 2-3 minutes until translucent.
Reduce heated to medium-low. Stir in the chopped fresh tarragon.
Add the cream and continue to whisk until lightly simmering.
If desired, whisk in 1/8 tsp of xanthan gum to thicken the sauce.
Continue whisking for 1-2 minutes until the sauce has thickened.
Serve the pan fried fish with the tarragon cream sauce.
Enjoy!