Make the meatballs: Pulse the bread in a food processor to make fine crumbs. Add the milk and Worcestershire sauce and pulse to make a paste; set aside.
Heat the butter and vegetable oil in a large nonstick skillet over medium heat; add the shallots and cook, stirring, until golden brown, about 8 minutes. Add the apple, garlic, cinnamon, 1 teaspoon salt and a few grinds of pepper and cook until the apple is tender, about 3 minutes. Stir in the breadcrumb mixture and cook, stirring, until thickened, about 4 minutes. Transfer to a large bowl and let cool completely.
Add the turkey and egg to the bowl and beat with a mixer on lowspeed until well combined, about 4 minutes. Cover and refrigerate at least 30 minutes.
Preheat the oven to 425 degrees F and coat a baking sheet with cooking spray. Dampen your hands and form the meat mixture into 36 balls (about1 inch each). Arrange on the prepared baking sheet and bake until lightly browned, 15 to 20 minutes.
Meanwhile, make the gravy: Melt the butter in a medium saucepan over medium heat. Add the flour and whisk to make a smooth paste, about 3 minutes. Gradually whisk in the chicken broth, then add the Worcestershire sauce. Cook, whisking, until slightly thickened, about 5 minutes. Add the meatballs and simmer until firm and cooked through, about 10 minutes. Serve over mashed potatoes and top with parsley and/or chives.