Season chicken pieces with salt and pepper in a bowl, then set aside. Prepare all other ingredients.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add chicken pieces in a single layer without overcrowding (work in batches if needed). Cook for 3-4 minutes until golden brown, turning occasionally. Transfer to a plate and set aside.
Add remaining tablespoon of olive oil to the same skillet. Add onions and cook for 2-3 minutes until they begin to soften. Add garlic and cook for 30 seconds until fragrant.
Add bell peppers to the skillet and cook for 2 minutes, then add zucchini rounds, dried Italian herbs, paprika, and red pepper flakes if using. Cook for 3-4 minutes, stirring occasionally, until vegetables begin to soften but still maintain some firmness.
Return chicken to the skillet. Add chicken broth and lemon juice, stirring to combine all ingredients. Simmer for 4-5 minutes, or until chicken is cooked through and vegetables are tender-crisp. Season with additional salt and pepper if needed.
Remove from heat and sprinkle with freshly grated Parmesan cheese and chopped parsley. Cover for 1 minute to allow cheese to melt slightly. Serve directly from the skillet.