Preheat your oven to 425°F and position the rack in the center. Pat chicken pieces dry with paper towels, then toss with olive oil, salt, pepper, garlic powder, and paprika in a large bowl until evenly coated.
Heat a large cast-iron skillet or Dutch oven over medium-high heat for two minutes. Working in batches, sear the chicken pieces skin-side down for 3-4 minutes per side until golden brown, then transfer to a clean plate.
In the same skillet, melt butter and sauté the chopped onion for two minutes. Add minced garlic and sliced mushrooms, cooking another 2-3 minutes until fragrant and softened.
Return the seared chicken to the skillet, then add diced potatoes and sliced carrots around the pieces. Pour chicken broth over everything, then sprinkle dried thyme and rosemary evenly across the cozy baked chicken dinner.
Cover the skillet tightly with foil or a fitted lid, then transfer to the preheated oven. Bake for 35-40 minutes, checking that the chicken reaches 165°F internal temperature at the thickest part.
Remove the cover and increase oven temperature to 450°F for the final 8-10 minutes to crisp the skin slightly. The sauce should have reduced by half and vegetables should be fork-tender.