Preheat the oven to 375ºF.
Trim away the silver skin and any excess fat from the pork tenderloin using a thin, sharp knife. Pat the pork tenderloin dry with clean paper towels. Season the pork with kosher salt and black pepper.
Heat the dutch oven on the stove at medium-high heat. Add 1 tablespoon of olive oil and let the pan get hot (about 1-2 minutes).
Once the pan is hot, sear the pork tenderloin for 3-4 minutes per side, until the outside is slightly browned. After the pork is seared on all sides, turn off heat and set pork tenderloin aside on a plate.
Add the butter to the dutch oven and stir, making sure to scrape any browned bits from the pork tenderloin.
Add the balsamic vinegar and dried herbs, stirring until the butter is completely melted.
Place the pork tenderloin back into the dutch oven and spoon some sauce over it.
Place the dutch oven into the oven, lid on.
Cook until the pork tenderloin reaches an internal heat of 145ºF at the thickest part, about 10-15 minutes. I always check the internal temperature after 10 minutes.
After the pork tenderloin reaches the preferred internal temperature (145ºF is recommended), immediately remove the dutch oven from the oven. Remove the tenderloins from the dutch oven and onto a cutting board, leaving to rest for 10-15 minutes. Place aluminum foil over the top to keep warm.
While the tenderloin rests, spoon the pan juices into a small bowl for serving.
Once rested, slice into half-inch medallions. Place onto a serving plate or directly onto dinner plates.
Serve with the remaining pan sauce. Option to top with fresh herbs.