1. Cook the Pasta and Broccoli:

1. Bring a large pot of salted water to a boil.
2. Add the pasta and cook according to package directions, or until al dente.
3. Add the broccoli florets to the pot during the last 1 minute of cooking time. If using fresh broccoli, you may need to add it a few minutes earlier, depending on the size of the florets.
4. Drain the pasta and broccoli together and set aside.

2. Cook the Chicken:

1. While the pasta is cooking, heat the olive oil in a large pan or skillet over medium heat.
2. Add the minced onion and cook for 3-4 minutes, or until softened and golden.
3. Add the minced garlic and cook for just a few seconds, or until fragrant. Be careful not to burn the garlic.
4. Add the sliced chicken to the pan.
5. Season with salt and pepper.
6. Cook the chicken for 5-7 minutes, or until browned and cooked through. The internal temperature should reach 165°F (74°C).

3. Make the Sauce:

1. Reduce the heat to low.
2. Add the Parmesan cheese, light cream, pesto, salt, and pepper to the pan with the chicken.
3. Stir well to combine.
4. Simmer the sauce for 2-3 minutes, stirring occasionally, until it thickens slightly.

4. Combine and Serve:

1. Add the cooked pasta and broccoli to the pan with the sauce.
2. Stir gently until the pasta and broccoli are fully coated with the sauce.
3. Simmer for another 2-3 minutes to allow the flavors to meld.
4. Remove from heat and garnish with more Parmesan cheese, if desired.
5. Serve immediately.