Preheat oven to 425°F. Bring broth and farro to a boil in a saucepan over high. Reduce heat to medium-low; cover and simmer until farro is tender and liquid absorbed, about 25 minutes Remove from heat. Add lemon juice; fluff farro with a fork to combine.
Rub chicken breasts with cumin, turmeric, salt, and pepper. Heat oil in a large cast-iron skillet over medium-high. Place chicken in skillet, skin side down; cook until skin is golden brown, 4 to 6 minutes. Flip chicken breasts and transfer skillet to preheated oven. Bake until a thermometer inserted in thickest portion registers 165°F, 15 to 17 minutes. Let stand 3 minutes before cutting breasts in half diagonally.
While chicken cooks, stir together cashews, parsley, and lemon zest in a small bowl. Spread 1 tablespoon sour cream on each of 4 plates. Add 1/2 cup farro mixture, 1/2 chicken breast, and 2 tablespoons gremolata.