Prepare the tapenade: Soak the olives in warm water, 5 minutes; drain. Combine the olives, parsley, scallions, capers, garlic, mustard and olive oil in a food processor and pulse several times.
Prepare the meatballs: Put the ground beef in a large bowl and add 1/4 cup of the tapenade (reserve the rest for serving). Add the pimentos, breadcrumbs, egg and 1/2 teaspoon salt and mix with your hands until combined. Dampen your hands and form into 1 1/2-inch meatballs (about 24).
Heat the olive oil in a large nonstick skillet over medium-high heat. Add the meatballs and cook, turning, until browned on all sides, about 5 minutes; transfer to a plate. Add the tomato paste to the skillet and cook, stirring, until slightly darkened, about 1 minute. Add the chicken broth, brown sugar and vinegar and cook, stirring, until the sugar dissolves.
Return the meatballs to the skillet; reduce the heat to medium and simmer, occasionally spooning the liquid over the meatballs, until the liquid is reduced by half and the meatballs are cooked through, 30 to 40 minutes. Transfer to a platter. Serve with the reserved tapenade.