Soak wooden skewers in water for 20–30 minutes so they don’t burn.
Whisk mustard, honey, olive oil, lemon juice, soy sauce, garlic, paprika, salt, and pepper.
Reserve 2 tablespoons of the marinade for brushing later.
Toss chicken with remaining marinade. Cover and chill 20–30 minutes.
Preheat grill to medium-high. Clean and lightly oil the grates.
Thread marinated chicken onto soaked skewers, packing pieces snugly.
Grill 8–10 minutes, turning often, until lightly charred and 165°F inside.
Brush with reserved marinade during the last minute. Rest briefly, garnish with parsley, and serve.