Step 1: Preheat your oven to 400°F (200°C). Pat the pork tenderloin dry with paper towels and remove any silver skin. If desired, tie the thinner end with kitchen twine for even cooking.
Step 2: In a small bowl, combine the Dijon mustard, minced garlic, chopped fresh rosemary, thyme, salt, and pepper.
Step 3: Generously spread the mustard-herb mixture all over the pork tenderloin. Let it rest at room temperature for 15-20 minutes.
Step 4: Heat olive oil in a large oven-safe skillet (cast iron or stainless steel recommended) over medium-high heat until shimmering.
Step 5: Carefully place the seasoned pork tenderloin in the hot skillet and sear for 2-3 minutes per side, turning with tongs, until a golden-brown crust forms on all surfaces.
Step 6: Transfer the skillet with the seared pork to the preheated oven. Roast for 15-25 minutes, or until an internal temperature of 140-145°F (60-63°C) is reached in the thickest part of the meat. (The temperature will rise slightly during resting).
Step 7: Remove the skillet from the oven and transfer the pork tenderloin to a cutting board. Tent loosely with foil and let it rest for 5-10 minutes.
Step 8: While the pork rests, place the same skillet back on the stovetop over medium heat. Pour in the chicken or vegetable broth and scrape up any browned bits from the bottom of the pan with a wooden spoon. Simmer for 2-3 minutes, reducing the sauce slightly. Stir in optional butter if using.
Step 9: Slice the rested pork tenderloin into 1/2-inch thick medallions. Arrange on a serving platter and drizzle generously with the warm pan sauce. Serve immediately.