Stir together panko and milk in a large bowl. Let stand 5 minutes.

Meanwhile, place shallots and oil in a small saucepan. Cook over medium, stirring frequently, until lightly golden brown and crisp, 15 to 18 minutes. Using a slotted spoon, transfer shallots to a paper towel–lined plate. Sprinkle with ¼ teaspoon salt. Reserve shallot oil in saucepan.

Stir egg, onion powder, garlic powder, thyme, pepper, and remaining 1 ¼ teaspoons kosher salt into panko mixture until combined. Add chicken, and gently mix just until incorporated. Cover and refrigerate until mixture is firm enough to shape easily, about 15 minutes.

Shape mixture into 16 (about-2-tablespoon) meatballs. Heat 2 tablespoons of reserved shallot oil in a large nonstick skillet over medium. Add 8 meatballs, and cook, turning every 1 to 2 minutes, until browned on all sides and nearly cooked through, 7 to 8 minutes. Transfer meatballs to a plate. Repeat with remaining 8 meatballs. Do not wipe skillet clean.

Add chicken stock, apple butter, Dijon mustard, apple cider vinegar, and Worcestershire sauce to skillet. Bring to a simmer over medium. Cook, scraping browned bits from bottom of skillet, until sauce is glossy and reduced slightly, 3 to 4 minutes.

Return meatballs and any accumulated juices to skillet. Simmer, turning meatballs occasionally, until meatballs are cooked through and coated in sauce, about 2 minutes. Remove from heat. Push meatballs to one side, and whisk in butter, 1 piece at a time, until butter is melted and sauce is smooth and glossy.

Serve meatballs and sauce over mashed potatoes. Top with crispy shallots, chopped fresh chives, and black pepper.