01 - Preheat oven to 400°F (200°C) if using biscuit topping.
02 - In a large skillet over medium heat, heat olive oil. Add diced onion, carrots, and celery. Sauté for 4-5 minutes until beginning to soften. Stir in minced garlic and cook for 1 minute more until fragrant.
03 - Move the sautéed vegetables to one side of the skillet. Add the unsalted butter to the empty space and allow it to melt. Sprinkle the all-purpose flour over the melted butter and whisk to form a smooth paste. Cook for 1 minute, stirring constantly.
04 - Gradually pour in the low-sodium chicken broth and whole milk, whisking continuously to incorporate the roux and prevent lumps. Bring the mixture to a simmer and cook for 3-4 minutes, stirring occasionally, until the sauce has thickened.
05 - Stir in the shredded or diced chicken breast, frozen peas, thyme, salt, and black pepper. Allow the mixture to simmer gently for 2-3 minutes until the peas are heated through and the filling is creamy and well combined.
06 - Concurrently, separate the refrigerated biscuit dough and bake according to the package instructions. Alternatively, prepare the mashed potatoes if using as a topping.
07 - To serve, divide the warm chicken and vegetable filling evenly among individual serving bowls. Top each bowl with a freshly baked biscuit or a generous scoop of mashed potatoes. Serve immediately.