Preheat oven to 375°F. Grease a 9x13-inch baking dish and set aside.
In a large skillet over medium heat, melt butter. Add onion and cook until softened, about 5 minutes. Add garlic and cook for 1 minute more.
Sprinkle flour over the onion mixture and stir to coat. Cook for 2 minutes, stirring constantly.
Gradually whisk in chicken broth and heavy cream. Bring to a simmer and cook until thickened, about 5 minutes, stirring frequently.
Stir in cooked chicken, frozen vegetables, thyme, salt, and pepper. Cook for 2-3 minutes until vegetables are warmed through.
Pour the chicken mixture into the prepared baking dish and spread evenly.
Separate biscuits and cut each into quarters. Arrange biscuit pieces evenly over the top of the chicken mixture.
Bake for 25-30 minutes until biscuits are golden brown and the filling is bubbling around the edges. Let cool for 5 minutes before serving.