Preheat the oven to 400°F.
Heat the olive oil in a large oven-safe skillet over medium-high heat. Season the chicken with salt and pepper and cook for 5–6 minutes, until browned. Transfer to a plate.
Reduce the heat to medium. Add the onion and celery and cook for 4–5 minutes, until softened. Stir in the garlic and cook for 30 seconds.
Sprinkle the flour over the vegetables and stir for 1 minute to cook out the raw flavor.
Slowly whisk in the chicken broth, then the milk. Simmer for 3–4 minutes, stirring, until the sauce thickens.
Stir in the frozen vegetables, thyme, Dijon mustard, and the browned chicken. Season with salt and pepper.
Arrange the biscuit pieces evenly over the filling.
Bake for 15–18 minutes, until the biscuits are golden and cooked through and the filling is bubbling. Let rest 5 minutes before serving.