Melt the unsalted butter in a large skillet over medium heat. Add chopped onion and sauté until soft and translucent, about 3–4 minutes. Stir in minced garlic and cook for another 30 seconds.

Sprinkle in all-purpose flour and cook for 1 minute, stirring constantly. Gradually whisk in low-sodium chicken broth until smooth, then add whole milk. Simmer and stir frequently until thickened, about 5 minutes.

Mix in salt, black pepper, dried thyme, and dried parsley. Fold in shredded chicken and frozen mixed vegetables. Let everything simmer for another 4–5 minutes.

Preheat oven to 375°F (190°C). Grease a 9×13-inch baking dish and pour the chicken filling into it, spreading evenly.

Place refrigerated biscuits on top of the chicken filling, spacing them slightly.

Bake for 20–25 minutes until biscuits are golden. Cover loosely with foil if they brown too quickly.

Brush the tops of the biscuits with melted butter and sprinkle with fresh parsley just before serving.

Allow to cool for 5 minutes before serving.