Pat the chicken breasts dry and gently pound any very thick pieces to an even thickness so they cook evenly.
Mix the garlic powder, paprika, Italian seasoning, salt, and black pepper, then season both sides of the chicken evenly.
Heat the olive oil in a large skillet over medium-high heat until hot, then sear the chicken for about 4–5 minutes per side until golden. Transfer it to a clean plate.
Reduce the heat to medium and cook the onion, bell pepper, broccoli, and mushrooms for 6–8 minutes until they begin to soften and brown.
Stir in the minced garlic and cook for 30–60 seconds until fragrant, being careful not to burn it.
Pour in the chicken broth and scrape the browned bits from the bottom of the skillet so they become part of the sauce.
Stir in the butter, heavy cream, and dried thyme, then bring the mixture to a gentle simmer.
Add the Parmesan and simmer gently for 2–3 minutes until the sauce thickens slightly.
Return the chicken to the skillet and spoon the creamy sauce and vegetables over each breast.
Cover and simmer for 6–10 minutes until the chicken reaches 165°F (74°C) in the thickest part.
Check the sauce consistency and adjust with a splash of broth if too thick, or simmer uncovered briefly if too thin.
Taste and adjust the seasoning, then let the chicken rest in the sauce for 3–5 minutes.
Garnish with fresh parsley and serve the chicken with the vegetables and creamy sauce.