Preheat the oven to 375°F (190°C).
In a large skillet, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Add the minced garlic and cook for an additional minute until fragrant.
Stir in the shredded chicken, mixed vegetables, chicken broth, heavy cream, thyme, salt, and black pepper. Mix well and let simmer for about 5 minutes until heated through.
Pour the chicken and vegetable mixture into a 9x13 inch baking dish, spreading it evenly.
Open the biscuit dough and cut each biscuit into quarters. Arrange the biscuit pieces over the top of the casserole, covering it as evenly as possible.
Bake in the preheated oven for 25-30 minutes, or until the biscuits are golden brown and cooked through.
Remove from the oven and let cool for a few minutes before serving.