Prepare pork: Place the tenderloin on a cutting board, remove the fat and the silverskin with a small sharp knife. Slip the blade just under this skin, release a bit of it first. Grab this released piece with the other hand and run the knife underneath the skin, keeping it at an angle away from the meat. Work carefully to remove only the skin and not the flesh underneath. Now cut the filet in two equal parts.
Dry rub: Mix sweet and smoked paprika, garlic powder, salt, and pepper. Rub the meat well with the mixture.
Prepare vegetables: Peel and cut the potatoes into small cubes (about 1 ½ cm/ 0.6 inch), chop carrots and pepper into small cubes, finely chop the garlic cloves, set them aside. Finely chop the onion and set it aside separately from the rest of the veggies. Snap the green beans in two and set them aside separately from the rest.
Brown: Heat 1 tablespoon of the oil in a wide and shallow Dutch oven and brown the meat all over, about 2 minutes per side. Remove from the pot. Heat the remaining oil and cook the onions with a pinch of salt for about 2 minutes, stirring often.
Cook vegetables: Add the remaining vegetables except for the green beans, mix well, and scrape the pot's bottom. Cook for 5 minutes, often stirring, until the vegetables are slightly softer. Add a splash of the chicken stock if necessary to stop the vegetables from catching. .
Simmer: Stir in green beans, thyme, rosemary, and remaining stock. Nestle the two pork pieces on top. Cover, lower the heat, and cook for 15-20 minutes or until the internal temperature reaches 63 degrees Celsius/ 145 degrees Fahrenheit (Note 2). Remove the meat from the pot, let it rest while you finish cooking the dish
Gravy: Continue cooking the vegetables and the gravy with the lid on for another 5 minutes. Remove the cover and cook for another 5 minutes to allow the sauce to thicken and the potatoes to become soft (if they are not already).
Serve: Slice the meat, arrange on top of the veggies and potatoes and serve.