Preheat oven to 350 degrees.
Season the pork loin roast generously with salt and black pepper.
Heat the olive oil over medium-high heat in a Dutch oven.
Sear the pork roast 2-3 minutes per side or until golden brown on all sides, adjusting the heat as necessary so the oil doesn't smoke. Transfer the roast to a plate.
Place the shallots and garlic in the Dutch oven and cook for 3-4 minutes to brown and soften slightly.
Add the white wine and bring to a boil. Boil for 1-2 minutes, scraping up any browned bits.
Add the chicken broth, mustard, and thyme bundle. Bring to a simmer. Place the pork roast back in the Dutch oven, cover it with the lid slightly ajar, and place it in the oven.
Cook for 30 minutes. After 30 minutes, check the internal temperature. Turn the roast over and cook for another 20-30 minutes, or until the internal temperature reaches at least 145 degrees.
Transfer roast to a platter. Tent to keep warm and rest. Discard the thyme bundle. Place the Dutch oven back on the stove.
Place flour in a heat-proof bowl. Remove 1/2 cup liquid from the Dutch oven and add to flour. Whisk until smooth.
Pour the flour mixture into the braising liquid. Bring to a simmer and cook for 3-4 minutes or until thickened. Add the chopped parsley and add salt and black pepper if needed.
Remove the butcher's twine. Slice the roast into 1/2-inch (or so) slices and place on a serving platter. Pour some of the sauce over the roast and serve the remaining sauce on the side.