Heat the olive oil in a Dutch oven over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 5 minutes. Remove the chicken and set it aside.
Add the leeks, mushrooms, and carrots to the pot. Cook until the leeks soften and the mushrooms release their liquid, about 6 minutes. Stir in the 2 tablespoons of flour, thyme, salt, and pepper, and cook for 1 minute more.
Return the chicken to the pot and pour in the chicken stock. Bring the mixture to a simmer and cook for 15 minutes, stirring occasionally, until the broth thickens slightly.
While the stew simmers, prepare the dumplings. In a bowl, combine the 1 cup flour, cheddar cheese, baking powder, and 1/2 teaspoon salt. Stir in the milk and melted butter until a soft dough forms.
Drop spoonfuls of the dumpling dough evenly over the surface of the simmering stew. Cover the pot and cook for 12 minutes without lifting the lid, until the dumplings are puffed and cooked through.