Salt and pepper chicken on both sides. Heat the olive oil in a large skillet over medium-high heat and brown chicken on each side. (You'll need to work in batches.) Transfer the browned chicken to a paper towel-lined plate to drain. Once all the chicken is cooked, transfer it to a large casserole dish.
Preheat oven to 350 degrees F. In a medium bowl, whisk together the flour, chicken broth, and wine until smooth. Set aside.
To the same skillet, add mushrooms, onions, and garlic. Season with salt and pepper. Cook until the mushrooms are tender and the onions are soft.
Add the tomato paste to the skillet and stir to combine. Pour in the flour mixture, stir into the veggies, and bring to a boil. Continue cooking until thickened slightly. Add the tomatoes and adjust the seasoning if needed.
Pour the sauce over the chicken. Bake for 1 hour uncovered. Sprinkle parsley over top and serve warm.