Preheat the oven to 375°F (190°C).
Heat the olive oil in a large oven-safe skillet over medium heat. Add the onion and garlic and sauté for 3-4 minutes, or until the onion is soft and translucent.
Add the chicken, thyme, oregano, smoked paprika, salt, and pepper. Cook for 5-7 minutes, stirring occasionally, until the chicken is cooked through.
Add the mushrooms and cook for an additional 3 minutes.
Add the chicken broth and bring to a boil. Reduce the heat to low, cover the skillet with a lid, and simmer for 8-10 minutes.
In a small bowl, whisk together the heavy cream and flour until smooth. Add the cream mixture to the skillet and stir to combine. Bring the mixture to a boil and then reduce the heat to low. Simmer for 8-10 minutes, stirring occasionally, until the sauce is thickened.
Add the potatoes and stir to combine. Cover the skillet with the lid and transfer to the preheated oven. Bake for 30-35 minutes, or until the potatoes are tender.
Remove the skillet from the oven and sprinkle the Parmesan cheese over the top. Serve hot.