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Step 1
Arrange a rack in the upper third of the oven and heat the oven to 425°F. Line a rimmed baking sheet with aluminum foil coated with cooking spray or parchment paper.
Step 2
Stir 1/2 cup finely chopped fresh parsley leaves, 1/2 cup panko breadcrumbs, 1/4 cup of the half-and-half, 1 large egg, 1 teaspoon of the finely chopped fresh thyme leaves, 1 teaspoon of the minced garlic, 1 teaspoon of the kosher salt, and 1/4 teaspoon black pepper together in a large bowl.
Step 3
Add 1 1/2 pounds ground chicken and mix until evenly combined; do not overmix or the meatballs will be tough. Scoop out the mixture in heaping 2-tablespoon (1-ounce) portions (20 to and roll each between damp hands until a smooth ball forms. Place on the baking sheet, spacing them evenly apart.
Step 4
Roast until cooked through and an instant-read thermometer inserted in the center of a meatball registers at least 165°F, 12 to 15 minutes. Meanwhile, make the sauce.
Step 5
Melt 2 tablespoons unsalted butter in a 12-inch frying pan or skillet over medium-high heat. Add 8 ounces sliced cremini mushrooms and cook, stirring occasionally, until they’re tender, release their liquid, and begin to brown, 4 to 5 minutes.
Step 6
Add the remaining 1 1/2 teaspoons minced garlic, 1 1/2 teaspoons finely chopped fresh thyme leaves, and 2 tablespoons all-purpose flour. Cook, stirring constantly, for 30 seconds to cook the floury taste out.
Step 7
Whisk in the remaining 3/4 cup half-and-half, 1 1/4 cups low-sodium chicken broth, 1/4 cup Marsala wine, and the remaining 1/2 teaspoon kosher salt until the flour is dissolved and the sauce is smooth. Bring to a boil.
Step 8
Reduce the heat to maintain a simmer and cook, whisking occasionally, until the sauce thickens slightly and coats the back of a spoon, 4 to 5 minutes. Turn off the heat if the meatballs are not ready.
Step 9
When the meatballs are ready, turn on the broiler and broil until the meatballs are browned, 2 to 3 minutes. Transfer the meatballs to the sauce and gently stir to coat. Garnish with more finely chopped fresh parsley if desired.