Mix together salt, pepper, and allspice in a medium mixing bowl. Add turkey and gently mix with hands to combine, shape into 24 (1") balls.

Heat oil in a large nonstick skillet over medium high heat. Add meatballs and cook until browned, about 3 min, lower heat to medium and cook 3 more minutes, gently shaking pan. Using a slotted spoon, transfer meatballs to a plate.

Add broth to the same skillet, increase heat to medium high, and simmer until liquid is reduced by half, about 5 min. Whisk in sour cream and cook 1 min more. Add meatballs, sprinkle with parsley and serve hot.