Remove any large areas of silver skin (layer of white, opaque connective tissue on surface of the meat) from the pork if present. This can easily be removed by sliding a paring knife alongside the tissue to remove.
Drizzle the pork with 1 tbsp. olive oil and rub all over to coat evenly. Sprinkle evenly with the kosher salt and pepper.
Heat the remaining 1 tbsp. olive oil in a deep, oven-safe pan over high heat.
Sear each side of the pork until nice and golden, about 2-3 minutes per side. Once browned, remove from pan and set aside on a plate.
Add the onion wedges to the same pan. If there are not enough drippings from the pork, go ahead and add any more olive oil as needed. Cook the onion over medium-high heat until they start to brown.
While the onions are cooking, brush the tenderloin with the spicy mustard. Then, sprinkle the dried thyme and tarragon over the tenderloin until evenly coated.
Lay the tenderloin over the onions (make sure the pork is laying on top of the onions, not touching the bottom of the pan). Insert a meat thermometer into the deepest part of the tenderloin and place pan into the oven.
Roast until the pork reaches an internal temperature of 145 degrees, approximately 20-30 minutes.
Once 145 degrees, carefully remove from the oven. Heat the pan again over medium-high heat. Remove the pork once again and lay on a cutting board. Cover with aluminum foil for 5 minutes.
While the meat is resting, add the chicken broth to the onions and heat through. Using a wooden spoon, scrape any bits of goodness from the bottom of the pan and mix into the sauce.
To serve, slice the tenderloin across the grain (as pictured, into small rings) and slathered with tasty onions and sauce.