Place ground chicken into a large bowl. Finely mince 4 ounces mushrooms using a sharp knife or food processor. Add minced mushrooms to the chicken, along with panko breadcrumbs, Parmesan cheese, garlic, egg, parsley, salt, and pepper. Mix until evenly combined and form into approximately 24 meatballs, using a small cookie scoop.
Heat olive oil over medium heat in a large non-stick skillet. Brown meatballs, turning every 1 to 2 minutes until all sides are browned, about 8 to 10 minutes. Remove meatballs to a plate.
In the same skillet, heat remaining 1 tablespoon oil. Saute sliced mushrooms until browned, about 5 to 6 minutes. Add garlic and cook until fragrant, about 30 seconds. Whisk in marsala wine and chicken broth. Simmer over medium-low heat until liquid is reduced by a third to a half, 8 to 10 minutes.
Whisk cold butter into the sauce until melted, then pour in heavy cream. Continue simmering, stirring occasionally, until slightly thickened, about 8 to 10 minutes.
Return meatballs to the skillet and cook until meatballs are heated through, 2 to 3 minutes. Garnish with chopped parsley.
