Season the pork fillets on both sides with salt and pepper. Mince the tarragon and press it into one side of each fillet. You can do this up to an hour before cooking the pork, and leave it to rest at cool room temperature.
Slice the onion thinly. Heat a small frying pan over medium-low heat, add 1 tablespoon of olive oil, the sliced onion and a pinch of salt. Allow the onion to cook, mostly undisturbed for 5 – 6 minutes. The onion should be just starting to go golden when you start the pork.
Heat a cast iron skillet over medium-high heat. Add the remaining tablespoon of olive oil to the pan, then add the pork, herb-coated-side down. Cook for about 4 minutes, until starting to brown nicely. Flip the pork and continue cooking for another 4 – 6 minutes, until the internal temperature is 145°F.
Once you flip the pork, pour the water into the pan with the onions. Scrape up any browned bits on the surface of the pan, then add the the mustard and vinegar. Season to taste with salt and pepper. The water should reduce slightly to create a nice sauce.
Place a pork fillet on each plate, ladling the saucy onions over the top. Slice and enjoy.