Cook the pasta according to the instructions above, until al dente. Drain the pasta and set it aside.
In a large skillet or wok, heat 2 tablespoons of olive oil over medium-high heat.
Add the chicken pieces and cook for 5-7 minutes until golden brown and cooked through. Remove the chicken from the skillet and set it aside.
In the same skillet, add 2 tablespoons of butter and let it melt. Add minced garlic and cook for 1-2 minutes until fragrant.
Add 1 cup of chicken broth to the skillet, and bring it to a boil. Then, reduce the heat and let the broth simmer until it's reduced by half.
Add 1 cup of heavy cream to the skillet and whisk until combined.
Add 1 cup of freshly grated Parmesan cheese to the skillet and whisk until the cheese has melted and the sauce is smooth.
Add the blanched broccoli florets to the skillet and cook for 1-2 minutes, until the broccoli is heated through.
Add the cooked chicken to the skillet and stir to combine.
Add the cooked pasta to the skillet and toss until the pasta is well-coated with the sauce and chicken broccoli mixture.
Season with salt and pepper to taste.
Garnish with additional Parmesan cheese and serve hot.