Pat dry 4 chicken cutlets with paper towels; sprinkle both sides with ¼ teaspoon each salt and pepper.
Heat 1 tablespoon oil in a large cast-iron skillet over high heat.
Add the chicken; cook, undisturbed, until deeply golden brown, 2 to 3 minutes.
Reduce heat to medium-high; flip the chicken and cook, undisturbed, until an instant-read thermometer inserted into the thickest portion registers 160°F, 3 to 4 minutes.
Transfer to a clean cutting board and tent with foil to keep warm. Do not wipe the skillet clean.
Reduce heat to medium-low and add chopped onion; cook, stirring often, until softened, about 3 minutes.
Add minced garlic, ¼ teaspoon crushed red pepper and the remaining ½ teaspoon salt; cook, stirring constantly, until fragrant, about 1 minute.
Add 1¼ cups broth, scraping up any browned bits.
Stir in 2 packages rice; bring to a lively simmer over medium-high heat.
Cook until most of the liquid has been absorbed, about 4 minutes.
Remove from heat and stir in 5 ounces spinach in batches until wilted, 3 to 5 minutes.
Stir in thawed peas, warmed half-and-half, 2 tablespoons lemon zest, 2 tablespoons lemon juice and 2 tablespoons parsley.
Sprinkle with ½ cup goat cheese.
Slice the chicken and arrange over the rice mixture in a single layer.
Cover the skillet and let stand until the chicken is warmed through and registers 165°F, about 3 minutes.
Garnish with additional parsley, if desired.
