Combine the Italian seasoning, mustard powder, and red pepper flakes in a small bowl. Set aside.
Cut the chicken into ¾-inch cubes and season generously with lemon pepper seasoning.
Heat olive oil in a large skillet over medium-high heat.
Add the chicken and cook for 2–3 minutes per side until golden brown and cooked through. Remove and set aside.
Bring a large pot of salted water to a boil for the pasta.
In the same skillet, pour in the chicken broth and white grape juice mixture. Scrape up the browned bits from the bottom of the pan and let the liquid reduce by half, about 4 minutes.
Add butter and garlic. Cook for one minute until fragrant.
Stir in the flour and cook for another 1–2 minutes.
Slowly whisk in the chicken broth followed by the half-and-half.
Stir in the hot sauce and prepared seasonings.
Bring to a gentle boil, then reduce to a simmer.
Cook the penne according to package directions.
During the final 4 minutes of cooking, add the broccoli to the pasta water.
Drain the pasta and broccoli together.
Reduce the sauce to low heat and gradually stir in the Parmesan and Asiago until smooth.
Remove from the heat and stir in the fresh lemon juice.
Add the cooked chicken, broccoli, and pasta to the sauce.
Toss until everything is evenly coated. Serve your Chicken and Broccoli Pasta immediately with extra Parmesan if desired.