
Preheat the oven to 200C/390F, or 180C fan. Set a wire rack over a tray or plate so the pork can rest after cooking.
Pat the pork tenderloins dry, then season them evenly on all sides with the salt and black pepper.
Heat the oil in a large oven-safe skillet over medium-high heat. Add the pork and sear for about 5 minutes, turning to brown all sides evenly.
Transfer the skillet to the oven and roast for 12 to 15 minutes, or until the thickest part reaches 65C/149F for juicy pork with a faint blush in the center. For fully cooked pork with no pink, cook to 68C/155F.
Move the pork to the prepared rack and let it rest for 5 minutes before slicing. Resting helps keep the meat tender and juicy.
Place the same skillet over medium heat. Add the cream, Dijon mustard, and whole grain mustard, stirring well and scraping up the browned bits from the bottom of the pan.
When the sauce is hot, stir in the tarragon and parsley. Season to taste with a little extra salt and black pepper if needed. If the sauce is too thick, loosen it with 1 to 2 tbsp water. Do not let it boil hard.
Slice the pork into thick medallions and spoon the creamy mustard sauce over the top. Serve immediately.