Prep ingredients: Preheat oven to 450°F with a rack in upper 1⁄3. Peel and finely chop onion. Trim ends from carrots and celery; thinly slice. Tie remaining thyme leaves into a bundle using one of the thyme stems as twine.
Brown chicken: Pat chicken dry, trim any fat, and cut into 1-inch pieces. Season chicken with 1⁄2 teaspoon salt, and several grinds of pepper. Heat 1 tablespoon oil in a medium skillet over medium-high. Add chicken in a single layer and cook, without stirring, until well browned, about 3 minutes. Flip and brown on other side, about 2 minutes. Transfer chicken to a plate.
Cook vegetables: Add 1 tablespoon oil to same skillet over medium-high. Add carrot, onion, celery, thyme sprigs, and 1⁄2 teaspoon salt. Cook, covered, until vegetables are softened, about 3 minutes. Uncover and cook until vegetables are tender and browned, 2-3 minutes more. Add 2 tablespoons of the flour (save rest for step 5) and cook, stirring, about 1 minute.
Simmer stew: Return chicken and any accumulated juices to skillet along with 1⁄2 cup milk, chicken broth concentrate, and 1 cup water, scraping browned bits from bottom of skillet. Bring to a simmer. then remove skillet from heat, remove thyme sprigs, then stir in peas.
Make biscuits: In a medium bowl, combine 1⁄3 cup milk, 2 tablespoons oil, chopped thyme, 1⁄4 teaspoon pepper, and 1⁄2 teaspoon salt.Add remaining flour to bowl and stir just until evenly combined. Do not over mix.
Cook biscuits & serve: Dollop 10-12 level tablespoons of dough over stew. Transfer skillet to the upper oven rack and bake until lightly browned, 10-12 minutes. Let cool 5 minutes before serving.