Remove the meat from the refrigerator about 30 minutes before cooking.
Heat oil in a large casserole over high heat. Season the meat with salt and pepper, then brown on all sides, about 10 minutes total.
Reduce heat to medium and add a small amount of water. Put the lid on halfway.
Let the water simmer and evaporate completely. Turn the roast every 15–20 minutes and add small amounts of water as needed. Continue for about 1 hour.
Chop the onion, carrot, and celeriac (or celery stalks).
Add the vegetables to the pot and cook for 30 minutes over medium heat.
Add enough water to come about 2/3 of the way up the meat. Add a sprig of lovage if desired. Put the lid fully on.
Simmer for 1 hour. The pork is done when the thickest part reaches 63 °C / 145 °F with a meat thermometer.
Remove the meat from the pot and place it on a plate covered with foil to keep warm.
For the sauce, choose one method: Method A—strain through a sieve into another pot, mix cornstarch or flour with a little of the hot sauce until smooth, stir back in, simmer 5 minutes, season with salt and pepper. Method B—use a hand blender to purée the vegetables in the pot, add cornstarch or flour mixture if too thin, season with salt and pepper.
Slice the meat and serve with the sauce. Put extra sauce in a serving bowl on the side.