Boil salted water and cook pasta until al dente, adding broccoli during the last 3 minutes. Drain and set aside.
Mix all blackened seasoning spices in a small bowl.
Pat chicken dry, rub with olive oil, and coat evenly with seasoning.
Cook chicken in a hot skillet over medium high heat for 5 to 6 minutes per side until charred and cooked through, then rest and slice.
In the same skillet, melt butter, sauté garlic briefly, add cream, and simmer. Stir in Parmesan until smooth.
Season sauce with salt and pepper, thinning with pasta water if needed.
Toss pasta, broccoli, and tomatoes in the sauce until coated and warmed.
Top with sliced chicken, garnish with parsley, and serve warm.