Preheat the oven to 400°F (200°C).
In a large oven-safe skillet or Dutch oven, melt 2 tablespoons of unsalted butter over medium-high heat.
Add the diced chicken pieces and cook until lightly browned and no longer pink in the center, about 5-6 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion, carrots, and celery. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Sprinkle 1/4 cup of all-purpose flour over the vegetables and stir well to coat. Cook for 1-2 minutes to remove the raw flour taste.
Gradually whisk in 2 cups of chicken broth and 1 cup of whole milk, stirring constantly to prevent lumps.
Bring the mixture to a simmer and cook until thickened, about 3-5 minutes.
Stir in the cooked chicken, thawed peas, 1 teaspoon dried thyme, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Mix well and remove the skillet from heat.
In a medium bowl, combine 1 1/2 cups all-purpose flour, 2 teaspoons baking powder, and 1/2 teaspoon salt.
Add the 6 tablespoons of cold unsalted butter cubes to the flour mixture. Using a pastry cutter or your fingers, cut the butter into the flour until the mixture resembles coarse crumbs.
Pour in 3/4 cup whole milk and stir until just combined to form a soft dough.
Drop spoonfuls of the biscuit dough evenly over the chicken and vegetable filling in the skillet.
Place the skillet in the preheated oven and bake for 20-25 minutes, or until the biscuit topping is golden brown and cooked through.
Remove from the oven and let cool for 5 minutes before serving.