In a large skillet, melt half of the butter over medium heat. Once sizzling, add the chopped broccoli and sauté for about 5 minutes until tender-crisp and bright green. Stir in minced garlic and cook for an additional minute, then remove from pan.

In the same skillet, pour in the heavy whipping cream, bringing it to a gentle simmer over medium-low heat. Stir in half of the mozzarella cheese along with all the grated parmesan until melted and smooth, about 3-4 minutes. Season with salt and pepper to taste.

Return the cooked chopped chicken and sautéed broccoli to the skillet, stirring them into the creamy mixture. Allow everything to simmer together for about 2-3 minutes, ensuring that the chicken is heated through.

Top evenly with the remaining mozzarella cheese. Cover and cook on low heat for an additional 3-5 minutes, until the cheese is melted and bubbly.

Give a gentle stir to combine all flavors and serve warm directly from the skillet.