Preheat the oven to 350ºF. Spray a large baking dish with nonstick cooking spray.

Bring a large pot of salted water to a boil. Add the pasta and cook until al dente. Drain and set aside.

Meanwhile, heat the olive oil in a sauté pan over medium-high heat. Season the chicken with salt and pepper, and add it to the pan. Cook until browned and cooked through.

In a large bowl, beat together the cream cheese and egg. Stir in the 4 oz Mozzarella, 1/2 cup Parmesan and parsley. Add the chicken and the broccoli and stir until combined.

Fill each of the shells with a large spoonful of the filling. Place in the prepared baking dish. Set aside.

In a large sauté pan, melt the butter. Add the garlic and cook for 30-60 seconds, until fragrant. Whisk in the cream. Bring the mixture to a simmer, then add the half of the Mozzarella and the Parmesan. Simmer for 5-10 minutes, whisking occasionally, until slightly thickened. Season to taste with salt and pepper.

Pour the sauce over the top of the prepared shells. Top with the remaining Mozzarella cheese. Cover the baking dish with foil and bake for 30 minutes, then uncover and cook an additional 10-15 minutes, until the sauce is bubbling.

Remove from the oven and let sit for 10 minutes before serving.