In a large pot of boiling salted water, cook pasta according to package instructions. Within the last 2 minutes of cooking time, add broccoli; drain well.

Heat olive oil in a large skillet over medium high heat. Season chicken breasts with salt and pepper, to taste. Add to skillet and cook, flipping once, until cooked through, about 3-4 minutes per side. Let cool before dicing into bite-size pieces.

Melt butter in the skillet over medium heat. Whisk in flour until lightly browned, about 1 minute. Gradually whisk in chicken broth and milk, and cook, whisking constantly, until incorporated, about 1-2 minutes. Stir in heavy cream and garlic powder until slightly thickened, about 1-2 minutes.

Stir in Parmesan until well combined, about 1 minute. If the mixture is too thick, add more milk as needed.

Stir in pasta, broccoli and chicken. Gently toss to combine; season with salt and pepper, to taste.

Serve immediately, garnished with parsley, if desired.