In a large, wide-bottom saucepan, bring vegetable or chicken broth to a boil. Add 2 teaspoons pepper and 1 teaspoon salt, plus thyme. Lay chicken flat in broth, reduce to simmer, and cook for 15 minutes, turning once halfway through.
Remove saucepan from heat, and allow chicken to rest in broth for 5 minutes. Remove chicken and cut into bite-sized pieces. Discard thyme. Remove broth and reserve
Preheat oven to 350 degrees.
While chicken cooks, melt 1/2 Tablespoon butter in large skillet. Add mushrooms and saute over medium-low heat for 10 minutes. Remove from skillet and set aside
Melt 1 Tablespoon butter or avocado oil in same skillet. Add onion, celery and carrots, and saute over medium-low heat for 10 minutes. Add garlic and saute for 5 minutes
Melt 2 Tablespoons butter in saucepan used for chicken. Sprinkle flour into saucepan and whisk constantly, until smooth, about 2 minutes. Slowly add in reserved broth, whisking occasionally, for 3 minutes. Slowly add in milk, whisking occasionally for 3 minutes, until sauce is thickened. Season with 2 teaspoons fresh-cracked black pepper and 1 teaspoon sea salt
Spray baking dish(es) with cooking spray. Fold chicken, vegetables, and peas into sauce. Pour mixture into baking dish(es), top with biscuits, and bake
NOTE: This will be scorching hot, so make sure to let Biscuit Chicken Pot Pie rest for about 5 minutes before serving