Prepare the Meatball Mixture: Combine ground chicken, breadcrumbs, egg, grated Parmesan cheese, minced garlic, salt, black pepper, and dried thyme in a large bowl. Mix until just combined; over-mixing can lead to tough meatballs.

Form and Sear the Meatballs: Shape the mixture into uniform meatballs about one inch in diameter. Heat olive oil in a large skillet over medium heat and carefully add meatballs, searing them until golden brown on all sides.

Cook the Mushrooms: Once browned, remove the meatballs from the skillet and set aside on a plate. In the same skillet, melt butter then add sliced mushrooms and minced garlic; sauté until mushrooms are tender and beginning to brown.

Create the Sauce: Pour in heavy cream and chicken broth into the skillet with mushrooms, stirring well to combine all ingredients. Allow it to simmer for about five minutes until slightly thickened.