Bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente, usually about 9-11 minutes. Drain the pasta and set it aside while you prepare the chicken and sauce.
Heat the olive oil in a large skillet over medium-high heat. Add the diced chicken breasts, seasoning them with salt, pepper, oregano, basil, thyme, and red pepper flakes. Cook the chicken for about 5-7 minutes, stirring occasionally until browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and cook for 30 seconds to 1 minute until fragrant, being careful not to burn it. Pour in the chicken broth and scrape any browned bits from the bottom of the pan—this adds so much flavor!
Stir in the halved cherry tomatoes and cook for 3-4 minutes until they start to soften. Then toss in the fresh spinach leaves and cook until wilted, about 2 minutes.
Return the cooked chicken to the skillet and add the drained penne pasta. Toss everything together so the pasta is coated with the garlicky, herb-infused sauce. Sprinkle in the grated Parmesan cheese and stir until melted and creamy.
Finish with a generous sprinkle of freshly chopped parsley for a pop of color and freshness. Serve hot.