In a small saucepan, heat the stock along with the porcini to soften, 10 to 15 minutes. Scoop out the mushrooms and chop them, reserving the soaking liquid in the pan.
Season the chicken with salt and black pepper on both sides and dredge lightly in flour. In a large Dutch oven, heat the oil (2 turns of the pan) over medium-high heat. Working in two batches, add the chicken and brown until crispy on both sides. Transfer the chicken to a plate.
To the pan drippings, add the cremini and cook until browned. Add the onion, garlic, and red pepper flakes and stir to soften, 5 to 6 minutes. Add the wine, stir to deglaze the pan, and cook to reduce by half. Hand-crush the tomatoes as you add them to the pan, then add the juices from the cans. Add the roasted pepper (if using), basil, and chopped reconstituted porcini. Carefully pour in the mushroom soaking liquid, leaving the last few spoonfuls in the pan as grit may have settled there. Cook the sauce at a gentle bubble for 20 to 30 minutes to thicken a bit.
Return the chicken to the pan and simmer until the chicken is cooked through, 20 to 30 minutes.
Transfer the chicken to a warm serving platter and cover with half the sauce. Garnish with the parsley.
Pass extra sauce at the table.
TIP: I like to serve cacciatore with hearty whole wheat or farro spaghetti. Cook 1 pound pasta in boiling salted water and reserve 1 cup of the starchy cooking water before you drain it. Then toss the drained pasta with 2 tablespoons butter, half the cacciatore sauce, lots of grated pecorino cheese, and the starchy water. To serve the pasta as a first course, just cover the chicken with foil and keep it warm in a low oven.