Place the rice in a large microwave-safe bowl and add 1 cup water. Cover with plastic wrap, pierce with a knife a few times to vent, then microwave until the water is almost absorbed, 10 minutes. Uncover and fluff the rice with a fork; let cool completely.
Lightly beat 1 egg in a small bowl. Add to the bowl with the rice along with the lamb, beef, provolone, onion, half each of the mint and parsley, the marjoram, garlic, allspice, 1 teaspoon salt and 1/2 teaspoon pepper. Mix with your hands until just combined (do not overmix); cover and refrigerate 30 minutes.
Dampen your hands and form the meat into 18 balls (about 1 1/2 inches each). Bring the chicken broth to a boil in a large pot or Dutch oven. Add the meatballs, cover and cook over medium heat until tender, about 30 minutes, turning halfway through.
Whisk the remaining 2 eggs and the lemon juice in a small bowl until frothy. Remove 1 cup broth from the pot and gradually whisk it into the egg mixture. Push the meatballs to one side of the pot; reduce the heat to low and pour the egg mixture into the other side. Cook, stirring gently, until the sauce thickens slightly, about 4 minutes. Remove from the heat and stir in the remaining mint and parsley; season with salt and pepper. Serve the meatballs and sauce in shallow bowls. Top with arugula, drizzle with olive oil and season with salt and pepper.
Photograph by Christina Holmes
Recipe courtesy Food Network Magazine