Put the dried mushrooms in a heatproof bowl and pour boiling water over them to cover. Let sit for 30 minutes, until softened. Set a strainer over a bowl and line it with cheese cloth or a piece of paper towel. Drain the mushrooms in that strainer, capturing the soaking liquid. Rinse the mushrooms in several changes of water, squeeze out excess water and chop coarsely. Set aside. Measure out 1/4 cup of the soaking water and set it aside.
Heat 2 tablespoons of the olive oil over medium-high heat in a large, heavy nonstick skillet (I use cast iron). Season the chicken pieces generously with salt and pepper and brown on both sides until golden. Transfer the pieces to a plate when they are done. Pour off the fat from the pan and discard.(You can prep the vegetables while you are browning the chicken.)
Turn the heat to medium and add the remaining 1 tablespoon olive oil. The add the onion, carrot and celery. Cook, stirring until the vegetables begin to soften, about 5 minutes. Add the garlic and parsley, rosemary, pepper flakes and a good pinch of salt. Cover, turn the heat to low and cook, stirring often, for 5 to 10 minutes, until the mixture is soft and aromatic. Stir in the fresh and dried mushrooms and another pinch of salt. Turn the heat back to medium and cook, stirring, until the mushrooms are just tender, about 5 minutes. Stir in the wine and bring to a boil. Cook, stirring, for a few minutes until the wine has reduced by about half. Add the tomatoes and salt and pepper to taste.
Cook over medium heat, stirring often for 5 to 10 minutes, or until the tomatoes have cooked down a little and smell fragrant. Stir in the reserved mushroom soaking liquid. Taste and adjust the salt and pepper again.
Return the chicken pieces to the pan and make sure they are well submerged in the tomato mixture. Simmer over medium heat, partially covered for 30 minutes or until the chicken is tender. Taste the sauce, adjust the seasoning and serve with pasta or polenta