Season 4 chicken cutlets with ½ teaspoon pepper, ¼ teaspoon salt and 1 teaspoon lemon zest. Heat 2 tablespoons oil in a large skillet over medium-high heat until shimmering, about 30 seconds. Add the chicken; cook, undisturbed, until golden brown and cooked through (an instant-read thermometer inserted in the thickest part registers 165°F, about 5 minutes per side). Transfer to a clean cutting board. Do not wipe the skillet clean.

Add sliced cabbage, chopped shallots and the remaining 1 teaspoon lemon zest to the skillet. Cover and cook over medium-high heat, stirring occasionally, until the cabbage is tender, 12 to 15 minutes. Transfer the mixture to a plate. Do not wipe the skillet clean.

Add the remaining 1 tablespoon oil to the skillet; heat over medium heat. Add minced garlic; cook, stirring constantly, until fragrant, about 30 seconds. Add 1½ cups orzo; cook, stirring often, until lightly toasted, about 1 minute. Stir in ¼ cup lemon juice and the remaining ¼ teaspoon salt; cook, stirring constantly, until the liquid has almost evaporated, about 1 minute.

Add 3 cups broth; bring to a lively simmer. Reduce heat to maintain a gentle simmer; cook, stirring occasionally, until the orzo is tender, about 10 minutes. Remove from heat. Add ½ cup Pecorino, ¼ cup half-and-half and 2 tablespoons butter; stir until creamy and the butter is melted, about 1 minute.

Slice the chicken. Fold the cabbage mixture into the orzo and arrange the sliced chicken on top. Cover the skillet and let stand until the chicken is warmed through, about 3 minutes. Sprinkle with 2 tablespoons chives. Garnish with additional Pecorino, if desired.