Step 1

Preheat the oven to 350 degrees F. Heat the olive oil in a large pot over medium-high heat. Add the carrots, onion, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until the vegetables soften, about 5 minutes. Add the farro and cook, stirring, until toasted, 1 minute. Add the chicken broth and 3 cups water; cover and bring to a boil. Add the lemon zest, reduce the heat to medium low and simmer, uncovered, until the farro is almost tender, about 15 minutes. Stir in the chicken.

Step 2

Whisk the eggs and lemon juice in a bowl; drizzle 1/2 cup of the hot broth into the eggs, whisking constantly. Gradually stir the hot egg mixture into the pot. Cook over medium-low heat, stirring constantly, until thickened, about 3 minutes. Season with 1/4 teaspoon salt.

Step 3

Combine the feta and dill in a small bowl; season with salt and pepper. Fill the pita halves with the feta mixture and lightly brush with olive oil. Transfer to a baking sheet and bake until the cheese melts, 2 to 3 minutes. Top each serving of soup with more dill; season with pepper. Serve with the stuffed pitas.