Prepare pasta shells according to package directions until pasta is al dente; drain and place pasta shells on baking sheet to cool, separating them so they don't stick together.

While pasta is cooling, prepare Alfredo sauce by combining butter, garlic, heavy whipping cream and milk in a pan set on medium heat. Stir ingredients and bring them to a low simmer (do NOT boil). Place egg yolks in a bowl, beat until blended, then temper the eggs (this slowly raises the temp. of the egg yolks to prevent them from scrambling when they hit the simmering Alfredo sauce). To temper eggs, add a spoonful of the hot Alfredo sauce to the egg yolks, whisking as you add. Repeat process with 3-4 more spoonfuls, one at a time, whisking while adding. Slowly drizzle egg yolk mixture into the Alfredo sauce, whisking as you add. Whisk mixture well; remove pan from heat.

Add 1/2 cup Mozzarella cheese and Parmesan cheese. Stir. Add salt and pepper; season to taste.

In mixing bowl, combine chicken, cooked broccoli and 1/2 cup Alfredo sauce. Stir. Place a couple spoonfuls of Alfredo sauce in the bottom of a 9x13 cake pan. Place a large spoonful of the chicken/broccoli mixture into each shell. Place filled shells on top of sauce in pan.

Spoon remaining sauce over the top of the shells; sprinkle with 1/2 cup mozzarella cheese.

Bake (uncovered) at 350 degrees for 25 minutes. When done, the cheese sauce will be bubbling, and cheese will be melted on top. Remove pan to wire rack; let shells cool a minute before serving. Transfer shells to individual serving plates and spoon remaining Alfredo sauce over the top. Garnish with dried parsley flakes. Serve and enjoy!