Bring a large pot of salted water to a boiling point.
Add whole wheat penne to the boiling water and cook for 6 minutes.
Add the broccoli florets to the pasta water and continue boiling for an additional 3 to 4 minutes until pasta is al dente and broccoli is tender-crisp.
Reserve 1/2 cup of the starchy pasta water before draining the pasta and broccoli in a colander.
In the same pot used for the pasta, heat olive oil over medium heat.
Add minced garlic and red pepper flakes to the oil, sautéing for 60 seconds until aromatic.
Pour in the chicken bone broth and shredded rotisserie chicken, stirring for 2 minutes until the chicken is thoroughly heated.
Return the drained pasta and broccoli to the pot.
Add Parmesan cheese, lemon juice, salt, and pepper to the mixture.
Toss all ingredients together, gradually adding the reserved pasta water to emulsify the sauce until it coats the pasta evenly.
Serve immediately while hot.