With the rack in the middle position, preheat the oven to 140°C (275°F).
Season the shanks with salt and pepper. Dredge lightly in flour to coat, shaking off any excess.
Heat the oil in a large Dutch oven over medium-high heat. Brown the shanks on both sides, in batches if necessary. Remove and set aside.
In the same Dutch oven over medium heat, soften the vegetables, adding oil as needed. Add the honey and deglaze with the port. Add the shanks and thyme. Bring to a boil, cover and transfer to the oven. Bake until the meat is tender enough to be cut with a fork, about 2 hours. Adjust the seasoning.