Preheat oven 400°F. Slice garlic head top off. Drizzle 1 tsp oil, wrap foil. Roast baking sheet 30 minutes soft. Squeeze cloves bowl mash fork.
Fill large pot salted water. Boil spaghetti 9 minutes al dente. Reserve 1 cup pasta water measuring cup. Drain colander.
Heat olive oil skillet medium-high measuring spoon. Season chicken cubes salt pepper measuring spoons. Sear batches tongs 4 minutes golden each side. Remove plate.
Lower heat medium. Add mashed roasted garlic skillet. Stir wooden spoon 1 minute. Pour chicken broth, cream, Italian seasoning. Simmer 5 minutes thick.
Return chicken skillet tongs. Stir parmesan melt creamy. Add spaghetti toss 2 minutes. Splash reserved pasta water glossy coat.