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Fill a large pot with water and bring to a boil over high heat.
In a medium bowl, toss diced chicken breast with 0.5 tablespoon olive oil, dried Italian seasoning, garlic powder, salt, and black pepper.
Add penne pasta to boiling water and cook until al dente, about 8–10 minutes.
During the last 3 minutes of pasta cooking, add fresh broccoli florets to the pot to steam.
Drain pasta and broccoli, reserving 0.5 cup of pasta water.
Heat 0.5 tablespoon olive oil in a large skillet over medium-high heat.
Add seasoned chicken to the skillet and cook, stirring occasionally, until browned and cooked through (internal temperature 165°F), about 5–7 minutes; transfer chicken to a plate.
Reduce heat to medium and add minced garlic to the skillet; sauté until fragrant, about 1 minute.
Pour chicken broth into the skillet and scrape up browned bits; simmer for about 1 minute.
Return pasta, broccoli, and chicken to the skillet and toss to combine.
Stir in grated Parmesan cheese and add reserved pasta water as needed to reach desired consistency.
Taste and adjust seasoning with additional salt and black pepper if desired.
Serve immediately, topped with extra grated Parmesan cheese.