Heat oil in an ovenproof pot over high heat.
Season lamb necks with salt and pepper.
Brown necks on all sides; remove from pot and set aside.
Drain off all but 2 tablespoons of fat from pot.
Add onion, garlic and red pepper flakes.
Sauté on medium heat until vegetables are tender, about 6 minutes.
Add wine, anchovy paste, capers and olives, then simmer until the liquid has almost evaporated.
Add the stock and tomatoes, stirring to combine all ingredients.
Add the necks back to the pot.
Bring to a boil on the stovetop before covering tightly and placing in a 325° oven. (Note: Usually no additional salt is needed due to the anchovy paste and capers.)
Turn the lamb necks after 1 hour; cover and place back in the oven for 1 more hour, or until meat is tender enough to fall off the bone.
Remove necks from braising liquid and set aside to cool.
When necks are cool enough to handle, shred the meat, discarding excess fat and the bone.
Add the meat back to the braising liquid, stirring to combine.
Warm gently over low heat and serve with rigatoni pasta.
Sprinkle each serving with chopped parsley and feta.