Preheat oven to 400°F (200°C). Slice top off garlic head, drizzle with olive oil, wrap in foil, and roast for 30-35 minutes until soft and golden.
Pat chicken breasts dry, rub with olive oil, coat evenly with blackening seasoning. Cook in a large skillet over medium-high heat for 5-6 minutes per side until internal temperature reaches 165°F. Let rest, then slice into strips.
Bring large pot of salted water to boil, cook fettuccine according to package instructions until al dente. Reserve ½ cup pasta water, then drain pasta.
In same skillet, melt butter over medium heat. Squeeze roasted garlic cloves into pan and mash until smooth. Slowly pour in heavy cream, stir constantly. Bring to gentle simmer, add Parmesan cheese, stir until melted and sauce thickens. Add reserved pasta water if needed. Season with salt and pepper to taste.
Add drained fettuccine to sauce and toss gently to coat. Plate pasta, top with sliced blackened chicken, garnish with chopped fresh parsley. Serve immediately.
