Heat the olive oil in a Dutch oven over medium heat. Add the turkey cubes and cook until lightly browned on all sides, about 5 minutes. Remove the turkey to a plate and set aside.
Add the mushrooms, pearl onions, and carrots to the same pot. Cook for 6 to 7 minutes until the vegetables start to soften and the mushrooms release their liquid.
Stir in the garlic and cook for 1 minute. Sprinkle the flour over the vegetables and stir for another minute to coat everything evenly.
Slowly pour in the chicken broth while stirring to avoid lumps. Return the turkey to the pot and add the thyme, salt, and pepper.
Bring the mixture to a simmer, then reduce the heat to low. Cover and cook for 25 minutes, stirring once or twice, until the turkey is cooked through and the stew has thickened.