Step 1 – Cook the Vegetables
Melt butter in a large skillet or oven-safe pan over medium heat. Add onion, carrots, and celery. Cook until softened. Stir in garlic and cook 1 minute more.
Step 2 – Make the Creamy Base
Sprinkle flour over veggies and stir to coat. Gradually whisk in chicken broth and milk until thickened into a creamy sauce. Season with thyme, salt, and pepper.
Step 3 – Add Chicken & Peas
Fold in shredded chicken and frozen peas. Mix well.
Step 4 – Top with Biscuits
Transfer mixture to a casserole dish (or keep in oven-safe skillet). Arrange biscuits evenly on top. Brush biscuits with beaten egg.
Step 5 – Bake Until Golden
Bake at 375°F (190°C) for 25–30 minutes, until biscuits are puffed and golden and filling is bubbling.
Step 6 – Serve
Scoop into bowls and enjoy warm.