Prepare the chicken breast by cutting it into 1-inch chunks and transferring them to a bowl. Season with Italian seasoning and set aside.
Heat 2 tablespoons of olive oil in a large skillet over medium heat. Add the broccoli and sautee for 4-5 minutes or until broccoli is tender, but still has a bite to it. Transfer the broccoli to a plate.
Return the skillet to the stove over medium heat. Add 2 tablespoons of olive oil and the chicken. Cook for 8-10 minutes tossing occasionally.
Add the butter and garlic to the pan and cook until fragrant.
Next, add the heavy cream, salt, pepper, nutmeg, and broccoli to the pan. Reduce heat to low and simmer for 5 minutes.
Fold in the parmesan cheese and remove from heat.
While the sauce is simmering cook the pasta. Bring a large pot of salted water to a boil. Cook the pasta according to package instructions, for about 10 minutes. Drain and transfer to the Alfredo sauce.
Garnish with more parmesan cheese and freshly cracked black pepper.