It's possible to have chicken, vegetables and sauce all cook in one skillet—talk about easy! The techniques in this recipe can also be used if you scale up the amount of ingredients and transfer them to a roasting pan to finish cooking in the oven. You can also substitute chicken breasts for thighs in this dish.
Preheat a 10- or 12-inch oven-safe skillet over high heat for about 3 minutes. While the skillet is heating, place the squash and halved potatoes in a medium bowl, add a tablespoon of water and cover tightly with plastic wrap. Microwave on high until fork-tender, 2 to 3 minutes.
Pat the chicken thighs dry with paper towels. Season generously with salt and pepper. Add butter and oil to the skillet and swirl or stir to coat the bottom. Place the thighs skin-side down and sear until golden brown, 3 to 5 minutes. Reduce the heat to medium-high if the thighs seem to be browning too quickly. Flip the thighs and cook the other side until GBD (golden brown and delicious), 3 to 5 minutes longer. Transfer the thighs to a plate and set aside.
Stir in the onions, garlic and thyme. Cook, stirring, until the onion is translucent, about 1 minute. Add the microwaved squash and potatoes; turn the potato halves so they're cut-side down to brown. Cook until the potatoes are well browned on the bottom, 2 to 3 minutes. Season with salt and pepper, stir, and add the apple and broccolini. Cook until the apple starts to soften, about 1 minute.
Spread the vegetables and apple out evenly and place the chicken on top. Transfer to the oven and bake until the thighs are cooked through and an instant-read thermometer inserted into the thickest part not touching bone register 165 degrees F, 10 to 15 minutes.
Meanwhile, for the quick gravy: Whisk together 1 tablespoon of broth with the cornstarch in a small bowl to create a slurry. Whisk in the remaining broth, cream and salt until combined.
When the chicken is done, remove the skillet from the oven with oven mitts. Add the gravy and stir until the gravy is incorporated, about 30 seconds. Enjoy!