Preheat oven to 325°. Cook onions and garlic in oil in a medium skillet over medium-low heat until soft, about 15 minutes.
Place lambs' necks in a roasting pan. Add onion mixture, tomatoes, and bay leaves. Season with salt and pepper. Cover with aluminum foil and cook for 2 hours. Remove from oven, add green beans, stirring to incorporate, re-cover, then return to oven for 1 hour more.
About 45 minutes before the lamb stew is done, make the polenta.
Remove stew from oven, uncover, discard bay leaves, and season to taste with salt and pepper. Serve stew spooned over polenta.
POLENTA: Combine cornmeal and 7 cups cold salted water in a large pot. (Adding cornmeal to cold water keeps polenta lump-free.) Bring to a boil over medium-high heat. Reduce heat to low and cook, stirring constantly with a wooden spoon, until polenta pulls away from the sides of the pot, 30 - 40 minutes. Add butter and stir until melted. Season to taste with salt and pepper.