1. Cut the chicken into bite-size pieces, season with lemon pepper, salt, and pepper.
2. In a large skillet, heat olive oil over medium-high heat and cook the chicken until golden brown. Set aside.
3. Bring a pot of salted water to a boil and cook the pasta until almost al dente. Add broccoli during the last 4 minutes. Reserve ½ cup pasta water, then drain.
4. In the same skillet, add white wine to deglaze and reduce by half. Add butter and garlic, cook for 1 minute. Stir in flour, cook 1-2 minutes.
5. Gradually add chicken broth and half and half, stirring continuously until it thickens. Add hot sauce, mustard powder, paprika, and other seasonings, bring to a simmer.
6. Stir in grated cheese, ensuring the sauce is not too hot to prevent graininess. Remove from heat and add lemon juice.
7. Combine pasta, broccoli, chicken, and a bit of reserved pasta water with the sauce, folding gently to coat. Adjust salt as needed.