Preheat oven to 350F.
Salt and pepper the individual lamb shanks, then dredge them in flour.
Place a heavy pot over medium high heat and, when hot, add enough butter to cover the bottom of the pan. Turn the heat down if the butter starts to brown. Place the lamb shanks in the pot and brown them on all sides, turning often with tongs. Remove the pot from the heat and place the shanks on a side dish, covering them with foil.
Remove any excess fat or grease from the pot, but leave a film of it on the bottom to cook the vegetables.
Return the pot to the burner and add the ramps, the carrots, and the celery. If necessary, add more butter in order to coat the veggies. Sauté the mixture, stirring for several minutes until lightly browned, then stir in the tomatoes. Raise the heat, add the thyme and bay leaf, and cook a few minutes more. The vegetables should be softened and the tomatoes should start to render their juices.
Return the shanks to the pot and pour in the veal and chicken stock and wine. Add enough liquid so that the ingredients are covered. Bring to a simmer, cover, and place in preheated oven.
The cooking time will vary from 45 minutes to an hour according to the size of the shanks that are used. The shanks are finished when the meat is tender enough to be pulled cleanly away from the bone.
Remove the cooked shanks from the pot, covering them to keep warm. Strain the contents of the pot and discard the solids. Reduce the liquid by about half by cooking uncovered over high heat, skimming off any fat that may rise to the surface. Taste and adjust the seasonings, then swirl in the 2 tablespoons of butter.
Serve with a garnish of minced chives.