Season each side of the chicken with salt and pepper. Add it to a medium saucepan along with the chicken broth and bring it to a gentle bubble with the lid cracked for 15 minutes, until cooked through. Remove the chicken and shred. Set aside and reserve the broth.
Vegetable and Gravy Preparation
Melt butter in a wide pan over medium heat and sauté onions, celery, and carrots for 5-6 minutes. Add garlic and seasonings, cook for 1 more minute.
Add flour and toss to coat. Cook for 2 minutes or until you can no longer smell raw flour.
Add ⅔ of the chicken broth in small splashes, stirring to incorporate. Add the half and half similarly.
Add chicken bouillon and soy sauce. Stir in shredded chicken.
Thicken the gravy if desired by boiling gently and then simmering.
Add frozen peas and stir to combine. Remove from heat.
Assembly and Baking
Transfer filling to a lightly greased 8 x 8-inch baking dish if skillet isn't oven safe.
Add the biscuits on top and bake according to biscuit instructions, or until golden and set.
Optional: Brush butter on top of biscuits at end and bake at 450° for 3-5 more minutes for added browning.
Notes
For a crispier bottom biscuit, bake biscuits separately on a baking sheet.