Bring a large pot of salted water to a boil. Add spaghetti and cook until al dente according to package directions. Drain well and set aside.

Heat the olive oil in a large skillet over medium heat. Add the minced garlic and cook until fragrant, about 30 seconds to 1 minute. Watch closely to avoid browning.

Add the shredded chicken to the skillet. Stir and cook for 2 to 3 minutes until the chicken is heated through.

Pour in the heavy cream and raise the heat to bring it to a gentle simmer. Let it bubble for a minute to thicken slightly.

Reduce heat to low. Add the shredded Monterey Jack cheese, salt, black pepper, and Italian seasoning. Stir continuously until the cheese melts and the sauce becomes smooth and creamy.

Add the cooked spaghetti to the skillet. Toss and fold the pasta into the sauce until every strand is coated. Heat for another minute so everything is well combined.

Serve immediately, sprinkled with chopped parsley for color and freshness.