Bring 3 quarts water to boil in a large saucepan.
Add orzo and 1 teaspoon salt and cook over medium heat until just tender, about 10 minutes.
Drain and toss with lemon zest, lemon juice, 1 tablespoon mint, 1 tablespoon dill, half of garlic, and 2 tablespoons oil; season with salt and pepper to taste.
Meanwhile, mash bread with yogurt in bowl until smooth.
Add beef, onion, remaining garlic, mint, and dill, 1 teaspoon salt, and 1/2 teaspoon pepper.
Form mixture into 1 1/2 inch balls (you should have 24).
Heat remaining 1/4 cup oil in 12-inch nonstick skillet over med-high heat until just smoking.
Add meatballs and cook gently, shaking pan and turning meatballs with tongs, until browned on all sides and cooked through, about 7 minutes.
Spoon orzo onto serving platter, top with meatballs, and sprinkle with feta; serve.