In a pot of boiling salted water, cook the pasta according to package directions. Drain and set side.

In a medium saucepan, heat the olive oil over medium-low heat. Add garlic and cook, stirring frequently, until the garlic is golden, 1 to 2 minutes.

Whisk in the flour until smooth, about 2 minutes.

Gradually whisk in the chicken broth, greek yogurt, milk, pepper, and nutmeg.

Bring to a low boil, stirring constantly.

Lower the heat and simmer, stirring gently, until the mixture thickens, about 3 minutes.

Stir in 3/4 cup parmesan.

Add cooked chicken and broccoli to sauce mixture, followed by the cooked pasta.

Toss to combine and serve with more parmesan, if desired.