Boil large pot of salted water for pasta.
Cook pasta according to package directions until al dente.
Heat olive oil in large skillet over medium heat.
Season chicken pieces with salt and black pepper.
Cook chicken until golden brown, about 6 minutes.
Remove chicken from pan and set aside temporarily.
Add bell peppers and zucchini to same skillet.
Cook vegetables for 4 minutes until slightly tender.
Add broccoli florets and minced garlic to pan.
Cook for additional 2 minutes until fragrant.
Return cooked chicken to the vegetable mixture.
Pour heavy cream over chicken and vegetables.
Add Parmesan cheese and stir until melted.
Drain pasta and add to chicken mixture.
Toss everything together until well combined.
Garnish with fresh basil leaves before serving.