Make clarified butter. Place 2 lbs butter in a sauce pan over low heat until melted. Allow to cook until the milk solids float to the top. Once the butter stops bubbling, use a spoon to skin the foam off the top of the butter, then discard. What remains is clarified butter!
Sauté the aromatics. Add 3 sprigs tarragon, garlic, and sliced chili (if using) to clarified butter, then warm over medium heat. Make sure the skillet is large enough to fit all pieces of cod in an even layer.
Poach the fish. Cut cod into 3 or 4 roughly equal sized pieces. Season cod on both sides with 1 tsp Kosher salt and ¼ tsp black pepper. Add the cod to the warm butter, then cover and poach until cooked through, about 6-10 minutes. Thinner pieces of cod (the tail) will finish cooking before the tenderloin (thicker piece). You can carefully remove the cooked cod with a large spatula or spoon and transfer to a plate or serving platter while the remaining pieces cook through. Meanwhile, make the tarragon aioli.
Make the tarragon aioli. Place the egg, minced garlic, and 4 tsp lemon juice into the bowl of a food processor fitted. With the motor running, slowly stream in ½ cup canola oil until the sauce has thickened up, about 30 seconds - 1 minute. Scrape down the sides as needed, process once more, then transfer to a bowl.
Finish with olive oil. Slowly stream in ½ cup extra virgin olive oil while whisking constantly until incorporated and thick.
Finish with fresh herbs. Add chopped 2 Tbsp tarragon, ½ tsp salt, and ⅛ tsp pepper, then mix to combine. Serve over poached cod. Garnish with chives, a tiny sprinkle of flaky sea salt, and some freshly cracked black pepper.