Preheat the oven to 300 degrees F.
Heat a large braiser pan over medium-high heat and add the oil. Sprinkle the lamb shanks all over with 2 teaspoons salt. When the pan and oil are hot, sear the shanks on all sides until deep brown, rotating often, about 8 minutes. Remove the lamb to a plate.
To the pan, add the carrots, celery, onions and garlic and cook, stirring often with a wooden spoon, until the vegetables are soft and beginning to brown, about 5 minutes. Add the oregano, rosemary and tomato paste and cook, stirring constantly, for 3 minutes to caramelize the paste. Deglaze the pan with the wine and simmer for 3 minutes. Stir in the chicken stock, then add the lamb shanks back to the pan. Bring to a simmer, reduce the heat to medium-low, and cover the pan.
Transfer the pan to the oven and cook until the lamb is fork tender, about 2 hours, turning the shanks halfway through.
Meanwhile, in a large bowl, whisk together the honey, Dijon and 1/4 teaspoon salt. Add the escarole and radicchio and toss well to coat. Arrange the bitter greens on a large serving platter.
When the lamb is tender, remove the shanks to the platter with the greens. Simmer the sauce until reduced slightly, an additional 10 to 15 minutes. Spoon some of the sauce over the lamb. Serve the remaining sauce on the side, for guests to help themselves. Finish the platter by grating some fresh horseradish over the lamb.