In a large bowl, mash the rice with a fork until smooth and pasty. Add the bread, ¼ cup of broth, 2 tablespoons of dill, 1½ teaspoons salt and 1 teaspoon pepper. Using your hands, mix and mash the ingredients to a paste.

Add the beef, egg yolk, half of the garlic and 1 teaspoon of oregano, then mix with your hands until the mixture is homogeneous. Divide into 12 portions, form into smooth balls and place on a plate. Refrigerate, uncovered, for about 10 minutes.

In a 12-inch nonstick skillet over medium-high, heat 2 tablespoons of oil until shimmering. Add the meatballs and cook without disturbing until lightly browned on the bottoms, about 3 minutes.

Carefully turn the meatballs and cook until browned on the second sides, about another 3 minutes. Add the remaining garlic and the remaining 1 teaspoon oregano and cook, stirring, until fragrant, about 30 seconds.

Add the remaining ¾ cup broth, then scrape up any browned bits. Bring to a simmer, then cover, reduce to medium-low and cook, gently stirring once or twice, until the centers reach 160°F, 5 to 7 minutes.

Using tongs, transfer the meatballs to a serving dish and tent with foil. Bring the liquid in the pan to a boil over medium-high and cook, stirring occasionally, until thick enough that a spatula drawn through it leaves a trail, 2 to 3 minutes.

Off heat, whisk in the remaining 3 tablespoons olive oil and the lemon juice. Taste and season with salt and pepper. Pour the sauce over the meatballs and sprinkle with the remaining 2 tablespoons dill.