Get your oven heating to 325°F while you prep the chicken. Use paper towels to thoroughly dry each piece — any lingering moisture will prevent proper browning. Season all sides generously with kosher salt and let it sit while you gather the other ingredients.
Warm a generous glug of olive oil in your heaviest Dutch oven or braising pot over medium-high heat. When the oil shimmers, carefully lay the chicken pieces skin-side down without crowding — work in batches if needed. Let them brown undisturbed for 4-5 minutes until the skin turns golden and releases easily. Flip and brown the other side, then transfer to a plate. Pour off all but a thin film of fat.
Cut the mushrooms into chunky quarters and add them to the same pot. They'll release moisture at first, but keep cooking until they shrink and develop some color, about 5 minutes. Pour in the vermouth and let it bubble away completely — this concentrates the flavor. Scrape up any browned bits while you're at it, then transfer the mushrooms to a bowl.
Drop the chopped onions into the pot with a pinch of salt. Cook them gently, stirring occasionally, until they turn soft and translucent — about 6-8 minutes. You want them sweet and mellow, not browned, so adjust the heat as needed.
Stir in the grated carrot, crushed tomatoes, tomato paste, red pepper flakes, and red wine along with any liquid the mushrooms released. Bring everything to a gentle simmer, stirring to dissolve the tomato paste completely. The sauce should look rich and unified.
Toss the chopped herbs with the cooked mushrooms and nestle this mixture back into the simmering sauce. Arrange the browned chicken pieces on top, skin-side up, along with any accumulated juices. Press a piece of parchment paper directly onto the surface — this prevents the top from drying out during the long braise.
Slide the covered pot into your preheated oven and let time work its magic. After about an hour, check that the chicken is fork-tender and the sauce has thickened to a rich consistency. If it needs more time, give it another 15-20 minutes. The chicken should practically fall off the bone when done.
⏱ 1 hr
Let the cacciatore rest for 10 minutes before serving — this helps the flavors settle. Spoon it over creamy polenta or buttered egg noodles, making sure everyone gets plenty of that luscious sauce. Finish with a sprinkle of fresh chopped parsley for color and brightness.