Bring a large pot of salted water to a boil and cook the high-protein pasta according to package instructions for al dente texture.
Add the broccoli florets to the boiling pasta water during the final 3 minutes of the pasta's cooking time.
Reserve 0.5 cup of the pasta cooking water, then drain the pasta and broccoli mixture.
In a large skillet, heat olive oil over medium heat and sauté the minced garlic for 60 seconds until fragrant but not browned.
Reduce the skillet heat to low and whisk in the Greek yogurt, chicken broth, and grated parmesan cheese until a smooth sauce forms.
Add the shredded rotisserie chicken, cooked pasta, and broccoli to the skillet.
Toss all ingredients together to coat, adding the reserved pasta water 1 tablespoon at a time if the sauce is too thick.
Season with lemon zest, salt, and black pepper then serve immediately.