Preheat your broiler to high. Line a baking sheet with foil and lightly oil it.
In a large bowl, combine the panko breadcrumbs, milk, and 1 tablespoon (15 ml) of the Marsala wine. Let the mixture sit for 5 minutes to soften the breadcrumbs.
Add the ground chicken, pecorino cheese, egg, parsley, 1/2 teaspoon of the kosher salt, and the black pepper to the bowl. Use your hands to gently mix until just combined.
Shape the mixture into 24 small meatballs, using about 1 tablespoon per meatball. Place them on the prepared baking sheet.
Broil the meatballs for 5 minutes, until they start to brown. They do not need to be fully cooked yet. Remove from the oven and set aside.
Heat 1 tablespoon (15 ml) of the olive oil in a large skillet over medium-high heat. Add the sliced mushrooms and cook for 5 minutes, stirring occasionally, until browned.
Stir in the minced shallot and the remaining 1/2 teaspoon of kosher salt. Cook for 2 more minutes.
Reduce the heat to medium. Stir in the flour and the remaining 1 tablespoon (15 ml) of olive oil. Pour in the remaining 1/3 cup (80 ml) of Marsala wine and stir to combine.
Whisk in the chicken broth. Bring the sauce to a simmer and cook for 5 minutes. Add the meatballs to the skillet and simmer for 5 more minutes. The chicken is safe to eat when it reaches an internal temperature of 165°F (74°C). Serve warm with extra pecorino cheese.